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A secondorder ADI difference scheme based on nonuniform meshes for the threedimensional nonlocal evolution problem Comput. Math. Appl. (IF 3.476) Pub Date : 20211020
Leijie Qiao, Wenlin Qiu, Da XuThis work constructs and analyzes a nonlocal evolution equation with a weakly singular kernel in threedimensional space. In the temporal direction, the CrankNicolson (CN) method and productintegration (PI) rule are employed, from which the nonuniform meshes are used to eliminate the singular behaviour of the exact solution at t=0. Then, a fully discrete scheme is obtained by the spatial discretization

A discontinuous PetrovGalerkin method for compressible NavierStokes equations in three dimensions Comput. Math. Appl. (IF 3.476) Pub Date : 20211018
Waldemar Rachowicz, Adam Zdunek, Witold CecotApplication of a Discontinuous PetrovGalerkin (DPG) method for simulation of compressible viscous flows in three dimensions is presented. The approach enables construction of stable schemes for problems with a small perturbation parameter. The main idea of the method is a weak formulation with a relaxed interelement continuity of the solution. The formulation satisfies the infsup condition with the

A virtual element method for the steadystate PoissonNernstPlanck equations on polygonal meshes Comput. Math. Appl. (IF 3.476) Pub Date : 20211015
Yang Liu, Shi Shu, Huayi Wei, Ying YangPoissonNernstPlanck equations are a nonlinear coupled system which are widely used to describe electrodiffusion processes in biomolecular systems and semiconductors, etc. A virtual element method with order k (k≥1) is proposed to numerically approximate the PoissonNernstPlanck equations on polygonal meshes. The error estimates in the H1 norm are presented for the numerical solution to the PoissonNernstPlanck

Further studies on numerical instabilities of Godunovtype schemes for strong shocks Comput. Math. Appl. (IF 3.476) Pub Date : 20211014
Wenjia Xie, Zhengyu Tian, Ye Zhang, Hang Yu, Weijie RenIn this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunovtype schemes for strong shocks. By conducting dissipation analysis of Godunovtype schemes and a sequence of numerical experiments, we are able to clarify that the instability may be attributed to insufficient entropy production inside the numerical shock structure. As a

On the wellposedness of Banach spacesbased mixed formulations for the nearly incompressible NavierLamé and Stokes equations Comput. Math. Appl. (IF 3.476) Pub Date : 20211014
Gabriel N. Gatica, Cristian InzunzaIn this paper we introduce and analyze, up to our knowledge for the first time, Banach spacesbased mixed variational formulations for nearly incompressible linear elasticity and Stokes models. Our interest in this subject is motivated by the respective need that arises from the solvability studies of nonlinear coupled problems in continuum mechanics that involve these equations. We consider pseudostressbased

A unified framework of high order structurepreserving Bsplines Galerkin methods for coupled nonlinear Schrödinger systems Comput. Math. Appl. (IF 3.476) Pub Date : 20211013
Paul Castillo, Sergio GómezUsing a general computational framework, we derive an optimal error estimate in the L2 norm for a semi discrete method based on high order Bsplines Galerkin spatial discretizations, applied to a coupled nonlinear Schrödinger system with cubic nonlinearity. A fully discrete method based on a conservative nonlinear splitting CrankNicolson time step is then proposed; and conservation of the mass and

Numerical analysis of the diffusiveviscous wave equation Comput. Math. Appl. (IF 3.476) Pub Date : 20211013
Weimin Han, Chenghang Song, Fei Wang, Jinghuai GaoThe diffusiveviscous wave equation arises in a variety of applications in geophysics, and it plays an important role in seismic exploration. In this paper, semidiscrete and fully discrete numerical methods are introduced to solve a general initialboundary value problem of the diffusiveviscous wave equation. The spatial discretization is carried out through the finite element method, whereas the

Fast image inpainting strategy based on the spacefractional modified CahnHilliard equations Comput. Math. Appl. (IF 3.476) Pub Date : 20211011
Min Zhang, GuoFeng ZhangThe solution strategy of the spacefractional modified CahnHilliard equation as a tool for the gray value image inpainting model is studied. The existing strategies solve the convexity splitting scheme of the vectorvalued CahnHilliard model by Fourier spectral method. In this paper, we constructed a fast solver for the discretized linear systems possessing the saddlepoint structure within bloc

Spectral discretizations analysis with time strong stability preserving properties for pseudoparabolic models Comput. Math. Appl. (IF 3.476) Pub Date : 20211012
Eduardo Abreu, Angel DuránIn this work, we study the numerical approximation of the initialboundaryvalue problem of nonlinear pseudoparabolic equations with Dirichlet boundary conditions. We propose a discretization in space with spectral schemes based on Jacobi polynomials and in time with robust schemes attending to qualitative features such as stiffness and preservation of strong stability for a more correct simulation

SoftFEM: Revisiting the spectral finite element approximation of secondorder elliptic operators Comput. Math. Appl. (IF 3.476) Pub Date : 20211007
Quanling Deng, Alexandre ErnWe propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of secondorder elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting a leastsquares penalty on the gradient jumps across the mesh interfaces from the standard stiffness bilinear form. This penalty bilinear form is similar to the known

Numerical and sensitivity computations of threedimensional flow and heat transfer of nanoliquid over a wedge using modified Buongiorno model Comput. Math. Appl. (IF 3.476) Pub Date : 20211005
Puneet Rana, Gaurav GuptaNumerical investigation of the threedimensional flow and heat transfer of 36 nm Al2O3–H2O nanoliquid over a wedge surface is carried out by utilizing the modified Buongiorno model (MBM). The boundary layer approximation is assumed to be valid. The thermophysical properties of Al2O3–H2O nanoliquid are deliberated in the study by modeling them through the use of correlations based on experimental data

An adaptive virtual element method for incompressible flow Comput. Math. Appl. (IF 3.476) Pub Date : 20211005
Ying Wang, Gang Wang, Feng WangIn this paper, we firstly present and analyze a residualtype a posteriori error estimator for a loworder virtual element discretization for the Stokes problem on general polygonal meshes. We prove that this estimator yields globally upper and locally lower bounds for the discretization error. Then, we extend the estimator to the NavierStokes problem. In order to deal with the case of small viscosity

BDDC algorithms for advectiondiffusion problems with HDG discretizations Comput. Math. Appl. (IF 3.476) Pub Date : 20211006
Xuemin Tu, Jinjin ZhangIn this paper, a preconditioned GMRES method is developed and analyzed for solving the linear system from advectiondiffusion equations with the hybridizable discontinuous Galerkin (HDG) discretization. The preconditioner is the balancing domain decomposition methods (BDDC), one of the most popular nonoverlapping domain decomposition methods. For large viscosity, if the subdomain size is small enough

Minimal residual spacetime discretizations of parabolic equations: Asymmetric spatial operators Comput. Math. Appl. (IF 3.476) Pub Date : 20211006
Rob Stevenson, Jan WesterdiepWe consider a minimal residual discretization of a simultaneous spacetime variational formulation of parabolic evolution equations. Under the usual ‘LBB’ stability condition on pairs of trial and test spaces we show quasioptimality of the numerical approximations without assuming symmetry of the spatial part of the differential operator. Under a stronger LBB condition we show error estimates in

Virtual element approximation of twodimensional parabolic variational inequalities Comput. Math. Appl. (IF 3.476) Pub Date : 20211001
D. Adak, G. Manzini, S. NatarajanWe design a virtual element method for the numerical treatment of the twodimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element method is based on the lowestorder virtual element space that contains the subspace of the linear polynomials defined on each element. The connection between the

Thermoelectromechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation Comput. Math. Appl. (IF 3.476) Pub Date : 20211001
Fatemeh Abbaspour, Hadi ArvinThis paper investigates on the buckling treatment of a three layered rectangular nanocomposite microplate resting on elastic foundation. The core is a laminated nanocomposite layer reinforced with graphene platelets bonded with two piezoelectric facesheets. The microplate is subjected to thermoelectromechanical loads. The governing equations are developed in the framework of the first order shear

The macroelement analysis for axisymmetric Stokes equations Comput. Math. Appl. (IF 3.476) Pub Date : 20210929
YoungJu Lee, Hengguang LiWe consider the mixed finite element approximation of the axisymmetric Stokes problem (ASP) on a bounded polygonal domain in the rzplane. Standard stability results on mixed methods do not apply due to the singular coefficients in the differential operator and due to the singular or vanishing weights in the associated function spaces. We develop new finite element analysis in these weighted spaces

Fast stable finite difference schemes for nonlinear crossdiffusion Comput. Math. Appl. (IF 3.476) Pub Date : 20210929
Diogo LoboThe dynamics of crossdiffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in realtime. We propose the use of two operator splitting schemes for nonlinear crossdiffusion processes in order to lower the computational load, and establish their stability properties using discrete L2 energy methods. Furthermore

Parallelized PODbased suboptimal economic model predictive control of a stateconstrained Boussinesq approximation Comput. Math. Appl. (IF 3.476) Pub Date : 20210929
Julian Andrej, Lars Grüne, Luca Mechelli, Thomas Meurer, Simon Pirkelmann, Stefan VolkweinMotivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the NavierStokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a suboptimal (but applicationally acceptable) solution with significantly

A partitioned solver for compressible/incompressible fluid flow and light structure Comput. Math. Appl. (IF 3.476) Pub Date : 20210927
Deepak Garg, Paolo Papale, Antonella LongoIn this work, a partitioned fluidstructure interaction solver is presented. Fluid flow problem is solved with timediscontinuous deforming domain stabilized spacetime finite element method. Flow is computed with pressure primitive variables which permit to use the same numerical technique for both compressible and incompressible regimes. Elastic deformation of the structure is modelled in the Lagrangian

Analysis of the local and parallel spacetime algorithm for the heat equation Comput. Math. Appl. (IF 3.476) Pub Date : 20210924
Dandan Xue, Yanren Hou, Yi LiIn this paper, a secondorder local and parallel spacetime algorithm is proposed and analyzed for the heat equation. This scheme is based on the parareal with spectral deferred correction method in time and the expandable local and parallel finite element method in space. It realizes the parallelism both in the temporal as well as in the spatial direction. We prove its stability and the optimal error

A pencil distributed direct numerical simulation solver with versatile treatments for viscous term Comput. Math. Appl. (IF 3.476) Pub Date : 20210922
Zheng Gong, Xudong FuWe present an efficient second or fourthorder finite difference direct numerical simulation (DNS) solver using pencillike domain decomposition parallel strategy, with the ability to handle different boundary conditions. The viscous term is treated implicitly, partial implicitly, or explicitly. The runtimes for different viscous treatments and different boundary conditions are evaluated quantitatively

An interpolationbased lattice Boltzmann method for nonconforming orthogonal meshes Comput. Math. Appl. (IF 3.476) Pub Date : 20210922
Nicolas Pellerin, Sébastien Leclaire, Marcelo ReggioWe propose an interpolationbased lattice Boltzmann formulation that is applicable to nonconforming orthogonal meshes. This interpolation configuration allows the use of localized and directional refinement that reduces mesh sizes and makes them well adapted for solving flows in various configurations, including aerodynamic shapes in free streams. The novel aspect of the proposed method lies in the

Viscoacoustic full waveform inversion: From a DG forward solver to a NewtonCG inverse solver Comput. Math. Appl. (IF 3.476) Pub Date : 20210916
Thomas Bohlen, Mario Ruben Fernandez, Johannes Ernesti, Christian Rheinbay, Andreas Rieder, Christian WienersFull waveform inversion (FWI) entails the illposed reconstruction of material parameters (such as sound speed and attenuation) from measurements of complete wave fields (full seismograms). In this paper we present a novel framework for FWI in the viscoacoustic regime. The new framework is based on a new elegant derivation of the system of state and adjoint PDEs which are approximated by the discontinuous

On the simulation of imagebased cellular materials in a meshless style Comput. Math. Appl. (IF 3.476) Pub Date : 20210915
S.M. Mirfatah, B. BoroomandA meshfree method on fixed grids is devised for simulation of Poisson's equation on 3D imagebased cellular materials. The nonboundary fitted discretization of such jagged voxel models of complex geometries is accomplished through embedding the microCT scan image in a Cartesian grid of nodes. The computational nodes inside the solid voxels are found by a simple pointinmembership test. Using a set

Recovering the aqueous concentration in a multilayer porous media Comput. Math. Appl. (IF 3.476) Pub Date : 20210913
Quan Pham HoangIn this paper, we consider an inverse problem for timefractional advectiondispersion equation in a multilayer composite medium. The main goal of our paper is to approximate the initial information, which is inaccessible for measurement, from the observation data at a certain point in second layer by constructing a regularized solution using a filter regularization method. Under appropriate regularity

A twolevel method for isogeometric discretizations based on multiplicative Schwarz iterations Comput. Math. Appl. (IF 3.476) Pub Date : 20210909
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. GasparIsogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of splinetype basis functions, that are able to hold a global smoothness and allow to exactly capture a wide set of common geometries. The current rise of this approach has encouraged the search of fast solvers for isogeometric discretizations

A new class of elliptic quasivariationalhemivariational inequalities for fluid flow with mixed boundary conditions Comput. Math. Appl. (IF 3.476) Pub Date : 20210909
Stanisław Migórski, Sylwia DudekIn this paper we study a class of quasivariationalhemivariational inequalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a implicit obstacle set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani–Ky Fan fixed point theorem. The applicability of

A preservative splitting approximation of the solution of a variable coefficient quenching problem Comput. Math. Appl. (IF 3.476) Pub Date : 20210910
Julienne Kabre, Qin ShengThis paper studies the numerical solution of a twodimensional quenching type nonlinear reactiondiffusion problem via dimensional splitting. The variable coefficient differential equation considered possesses a nonlinear forcing term, and may lead to strong quenching singularities that have profound multiphysics and engineering applications to the energy industry. Our investigations focus on the construction

Optimal l∞ error estimates of the conservative scheme for twodimensional Schrödinger equations with wave operator Comput. Math. Appl. (IF 3.476) Pub Date : 20210910
Xiujun Cheng, Xiaoqiang Yan, Hongyu Qin, Huiru WangIn this work, we consider the numerical computation for the twodimensional generalized nonlinear Schrödinger equations with wave operator. Based on the scalar auxiliary variable (SAV) approach, the original problem is transformed into an equivalent one, which corresponds to the energyconservation laws. We present an energyconserving and linearly implicit threelevel scheme for the equivalent system

Fourthorder compact difference schemes for the twodimensional nonlinear fractional mobile/immobile transport models Comput. Math. Appl. (IF 3.476) Pub Date : 20210908
Li Chai, Yang Liu, Hong LiIn this article, we develop fourthorder compact difference schemes based on the linearized generalized BDF2θ to solve the twodimensional nonlinear fractional mobile/immobile (M/I) transport equations. We derive theoretical results, including unconditional stability and error estimates associated with solution regularity. Finally, we provide extensive numerical examples with smooth solutions to demonstrate

A general finite element method: Extension of variational analysis for nonlinear heat conduction with temperaturedependent properties and boundary conditions, and its implementation as local refinement Comput. Math. Appl. (IF 3.476) Pub Date : 20210908
Xin Yao, Yihe Wang, Jianxing LengIn simulation of heat conduction with temperatureindependent physical properties and boundary conditions (BCs), Galerkin residual analysis and variational analysis yield equivalent finite element method (FEM), the conventional FEM. However, if the properties and BCs are temperaturedependent, it is discovered that their derivatives further induce nonlinearity of FEM which consequently generates divergence

A geometric characterization of PowellSabin triangulations allowing the construction of C2 quartic splines Comput. Math. Appl. (IF 3.476) Pub Date : 20210909
D. Barrera, S. Eddargani, M.J. Ibáñez, A. LamniiThe paper deals with the characterization of PowellSabin triangulations allowing the construction of bivariate quartic splines of class C2. The result is established by relating the triangle and edge split points provided by the refinement of each triangle. For a triangulation fulfilling the characterization obtained, a normalized representation of the splines in the C2 space is given.

Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures Comput. Math. Appl. (IF 3.476) Pub Date : 20210908
Paola F. Antonietti, Chiara Facciolà, Marco VeraniWe present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily

Effect of time integration scheme in the numerical approximation of thermally coupled problems: From first to third order Comput. Math. Appl. (IF 3.476) Pub Date : 20210906
E. Ortega, E. Castillo, R.C. Cabrales, N.O. MoragaThe advantages of using highorder time integration schemes for thermally coupled flows are assessed numerically. First, second, and thirdorder backward difference schemes are evaluated. The problem is solved in a decoupled manner using a nested iterative algorithm for the Navier–Stokes and energy equations to eliminate decoupling errors. For the space discretization, a stabilized finite element

Error bounds for portHamiltonian model and controller reduction based on system balancing Comput. Math. Appl. (IF 3.476) Pub Date : 20210902
Tobias Breiten, Riccardo Morandin, Philipp SchulzeWe study linear quadratic Gaussian (LQG) control design for linear portHamiltonian systems. To this end, we exploit the freedom in choosing the weighting matrices and propose a specific choice which leads to an LQG controller which is portHamiltonian and, thus, in particular stable and passive. Furthermore, we construct a reducedorder controller via balancing and subsequent truncation. This approach

Virtual elements for Maxwell's equations Comput. Math. Appl. (IF 3.476) Pub Date : 20210902
L. Beirão da Veiga, F. Dassi, G. Manzini, L. MascottoWe present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi and fullydiscrete schemes are considered. We derive optimal a priori estimates and validate them on a set of numerical experiments. As pivot results, we discuss some novel inequalities associated with de Rahm sequences of nodal, edge, and

A lockingfree finite element formulation for a nonuniform linear viscoelastic Timoshenko beam Comput. Math. Appl. (IF 3.476) Pub Date : 20210901
Erwin Hernández, Jesus VellojinIn this paper we use a modified constitutive law in a hereditary integral form to analyze the response of an isotropic nonuniform linear viscoelastic Timoshenko beam. A mixed method framework is used to provide stability and semidiscrete error estimates that do not deteriorate as the thickness parameter becomes small. Numerical experiments for both quasistatic and transient cases are presented.

A new geometric condition equivalent to the maximum angle condition for tetrahedrons Comput. Math. Appl. (IF 3.476) Pub Date : 20210902
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki, Takuya TsuchiyaFor a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant C that is smaller than π. Then, it is said to satisfy the maximum angle condition with the constant C. The maximum angle condition is important in the error analysis of Lagrange interpolation on tetrahedrons. This condition ensures that we can obtain an error estimation, even on certain

A construction of edge Bspline functions for a C1 polynomial spline on two triangles and its application to Argyris type splines Comput. Math. Appl. (IF 3.476) Pub Date : 20210902
Jan Grošelj, Marjeta KnezGiven two triangles in a planar domain sharing an edge and forming a convex quadrilateral, it is shown how to construct a nonnegative basis for C1 splines that restrict to polynomials of a total degree higher than one on each of the triangles. The representation may be seen as a generalization of the Bernstein–Bézier form of a spline on every separate triangle, and the main challenge in its development

Nonnegative moment fitting quadrature rules for fictitious domain methods Comput. Math. Appl. (IF 3.476) Pub Date : 20210831
Grégory LegrainFictitious domain methods enable to solve physical problems on unfitted grids, thereby avoiding timeconsuming and error prone meshing phases. However, an accurate integration of the weak formulation is still mandatory, leading to the need for efficient quadrature strategies in the elements that are partially located in the physical domain. Various methodologies have been proposed to this end. Among

A Finite Element Penalized Direct Forcing Immersed Boundary Method for infinitely thin obstacles in a dilatable flow Comput. Math. Appl. (IF 3.476) Pub Date : 20210831
Georis Billo, Michel Belliard, Pierre SagautIn the framework of the development of new passive safety systems for the second and third generations of nuclear reactors, the numerical simulations, involving complex turbulent twophase flows around thin or massive inflow obstacles, are privileged tools to model, optimize and assess new design shapes. In order to match industrial demands, computational fluid dynamics tools must be the fastest, most

Drug release from viscoelastic polymeric matrices  a stable and supraconvergent FDM Comput. Math. Appl. (IF 3.476) Pub Date : 20210830
J.S. Borges, J.A. Ferreira, G. Romanazzi, E. AbreuDrug release from viscoelastic polymeric matrices is a complex phenomenon where the main actors are the fluid, the polymeric structure and the drug. As the fluid enters into the polymer, the polymeric chains relax inducing a resistance to the fluid entrance. In contact with the fluid, a dissolution processes takes place and the dissolved drug diffuses through the medium. Our main goal in this paper

High performance computing of stiff bubble collapse on CPUGPU heterogeneous platform Comput. Math. Appl. (IF 3.476) Pub Date : 20210827
Remy Dubois, Eric Goncalves da Silva, Philippe ParnaudeauSCB is an efficient fluid solver developed for computing twophase compressible flows involving strong shocks and expansion waves. It solves a fourequation diffuseinterface model, which is derived from the fiveequation model proposed by Kapila et al. The governing equations are discretized by a finite volume method with explicit time stepping. SCB uses a fully parallel environment via Message Passing

Morley FEM for the fourthorder nonlinear reactiondiffusion problems Comput. Math. Appl. (IF 3.476) Pub Date : 20210825
P. Danumjaya, Ambit Kumar Pany, Amiya K. PaniNonconforming Morley finite element method is applied to a fourth order nonlinear reactiondiffusion problems. After deriving some regularity results to be used subsequently in our error analysis, Morley FEM is employed to discretize in the spatial direction to obtain a semidiscrete problem. A priori bounds for the discrete solution are derived and with the help of an auxiliary problem, optimal error

A Reduced Basis Method for a PDEconstrained optimization formulation in Discrete Fracture Network flow simulations Comput. Math. Appl. (IF 3.476) Pub Date : 20210824
Stefano Berrone, Fabio ViciniIn classic Reduced Basis (RB) framework, we propose a new technique for the offline greedy error analysis which relies on a residualbased a posteriori error estimator. This approach is as an alternative to classical a posteriori RB estimators, avoiding a discrete infsup lower bound estimate. We try to use less common ingredients of the RB framework to retrieve a better approximation of the RB error

On the spacetime discretization of variational retarded potential boundary integral equations Comput. Math. Appl. (IF 3.476) Pub Date : 20210824
D. Pölz, M. SchanzThis paper discusses the practical development of spacetime boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the spacetime cylinder. This approach conforms genuinely to the distinguished structure of the solution operators of the wave equation, socalled retarded potentials. Since the numerical

Solving steadystate liddriven square cavity flows at high Reynolds numbers via a coupled improved elementfree Galerkin–reduced integration penalty method Comput. Math. Appl. (IF 3.476) Pub Date : 20210824
Juan C. Álvarez Hostos, Joselynne C. Salazar Bove, Marcela A. Cruchaga, Víctor D. Fachinotti, Rafael A. Mujica AgelvisSteadystate twodimensional liddriven square cavity flows at high Reynolds numbers are solved in this communication using a velocitybased formulation developed in the context of the improved elementfree Galerkin–reduced integration penalty method (IEFG–RIPM). The analyses based on the IEFG–RIPM are performed under a standard Galerkin weakformulation, i.e. without the need of introducing streamlineupwind

A staggered discontinuous Galerkin method for elliptic problems on rectangular grids Comput. Math. Appl. (IF 3.476) Pub Date : 20210823
H.H. Kim, C.Y. Jung, T.B. NguyenIn this article, a staggered discontinuous Galerkin (SDG) approximation on rectangular meshes for elliptic problems in two dimensions is constructed and analyzed. The optimal convergence results with respect to discrete L2 and H1 norms are theoretically proved. Some numerical evidences to verify the optimal convergence rates are presented. Several numerical examples to the elliptic singularly perturbed

Pointwise error estimate of an alternating direction implicit difference scheme for twodimensional timefractional diffusion equation Comput. Math. Appl. (IF 3.476) Pub Date : 20210823
Yue Wang, Hu ChenAn alternating direction implicit (ADI) difference method is adopted to solve the twodimensional timefractional diffusion equation with Dirichlet boundary condition whose solution has some weak singularity at initial time. L1 scheme on uniform mesh is used to discretize the temporal Caputo fractional derivative. Pointwiseintime error estimate is given for the fully discrete ADI scheme, where the

An experimental comparison of a spacetime multigrid method with PFASST for a reactiondiffusion problem Comput. Math. Appl. (IF 3.476) Pub Date : 20210823
Pietro Benedusi, Michael L. Minion, Rolf KrauseWe consider two parallelintime approaches applied to a (reaction) diffusion problem, possibly nonlinear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and spacetime multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization

A computational method for model reduction in index2 dynamical systems for Stokes equations Comput. Math. Appl. (IF 3.476) Pub Date : 20210823
A. Chkifa, M.A. Hamadi, K. Jbilou, A. RatnaniOur aim through this paper is to describe a Krylov based projection method in order to reduce highorder dynamical systems. We focus on differential algebraic equations (DAEs) of index2 that arise from spatial discretization of Stokes equations. An efficient algorithm based on a projection technique onto an extended block Krylov subspace that appropriately allows us to construct a reduced order system

A priori and a posteriori error estimates of the weak Galerkin finite element method for parabolic problems Comput. Math. Appl. (IF 3.476) Pub Date : 20210819
Ying Liu, Yufeng NieWe derive the priori and a posteriori error estimates of the weak Galerkin finite element method with the CrankNicolson time discretization for the parabolic equation in this paper. The priori error estimates are deduced based on existing priori error results of the corresponding elliptic projection problem. For the a posteriori error estimates, the elliptic reconstruction technique is introduced

A rotationfree quadrature element formulation for free vibration analysis of thin sectorial plates with arbitrary boundary supports Comput. Math. Appl. (IF 3.476) Pub Date : 20210820
Deng'an Cai, Xinwei Wang, Guangming ZhouDue to corner stress singularities, free vibration analysis of thin sectorial plates with arbitrary boundary supports including a free vertex is a rather challenging problem. In this paper, a novel rotationfree quadrature element formulation based on Kirchhoff plate theory is presented to solve the problem. Different from all existing quadrature thin plate element formulations, rotational degrees

A parametrized level set based topology optimization method for analysing thermal problems Comput. Math. Appl. (IF 3.476) Pub Date : 20210820
Baseer Ullah, SirajulIslam, Zahur Ullah, Wajid KhanThis paper focuses on the utilization of local radial basis functions (LRBFs) based level set method (LSM) for topology optimization of twodimensional thermal problems using both concentrated as well as uniformly distributed heat generation. The design domain is embedded implicitly into a higherdimensional function, which is parametrized with the LRBFs through an explicit scheme. This novel combination

A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation Comput. Math. Appl. (IF 3.476) Pub Date : 20210820
Khemraj Shukla, Jesse Chan, Maarten V. de HoopWe introduce a new symmetric treatment of anisotropic viscous terms in the viscoelastic wave equation. An appropriate memory variable treatment of stressstrain convolution terms, result into a symmetric system of first order linear hyperbolic partial differential equations, which we discretize using a highorder discontinuous Galerkin finite element method. The accuracy of the resulting numerical

Improvement and application of weakly compressible moving particle semiimplicit method with kernelsmoothing algorithm Comput. Math. Appl. (IF 3.476) Pub Date : 20210818
Huiwen Xiao, YeeChung JinThe moving particle semiimplicit method (MPS) is a wellknown Lagrange method that offers advantageous in addressing complex fluid problems, but particle distribution is an area that requires refinement. For this study, a particle smoothing algorithm was developed and incorporated into the weakly compressible MPS (sWCMPS). From the definition and derivation of basic MPS operators, uniform particle

Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element Comput. Math. Appl. (IF 3.476) Pub Date : 20210819
S. Zghal, F. DammakThe novelty of the current study is the development of an enhanced finite shell model using the first order shear deformation theory (FSDT) to study the vibration characteristics of imperfect functionally graded (FGM) plates and shells including porosities. Unlike standard (FSDT) theory, the proposed model presents an improvement of the FSDT via the introduction of a quadratic shear function allowing

Sixth order compact finite difference schemes for Poisson interface problems with singular sources Comput. Math. Appl. (IF 3.476) Pub Date : 20210817
Qiwei Feng, Bin Han, Peter MinevLet Γ be a smooth curve inside a twodimensional rectangular region Ω. In this paper, we consider the Poisson interface problem −∇2u=f in Ω∖Γ with Dirichlet boundary condition such that f is smooth in Ω∖Γ and the jump functions [u] and [∇u⋅n→] across Γ are smooth along Γ. This Poisson interface problem includes the weak solution of −∇2u=f+gδΓ in Ω as a special case. Because the source term f is possibly

Negative norm estimates and superconvergence results in Galerkin method for strongly nonlinear parabolic problems Comput. Math. Appl. (IF 3.476) Pub Date : 20210817
Ambit Kumar Pany, Morrakot Khebchareon, Amiya K. PaniThe conforming finite element Galerkin method is applied to discretise in the spatial direction for a class of strongly nonlinear parabolic problems. Using elliptic projection of the associated linearised stationary problem with Gronwall type result, optimal error estimates are derived, when piecewise polynomials of degree r≥1 are used, which improve upon earlier results of Axelsson ((1977) [3]) requiring