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A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions
Author(s) -
Liu Yujie,
Wang Junping
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22440
Subject(s) - mathematics , finite element method , discretization , galerkin method , discontinuous galerkin method , mathematical analysis , maximum principle , weak formulation , scheme (mathematics) , convection–diffusion equation , mixed finite element method , boundary value problem , mathematical optimization , physics , thermodynamics , optimal control
Abstract This article establishes a discrete maximum principle (DMP) for the approximate solution of convection–diffusion–reaction problems obtained from the weak Galerkin (WG) finite element method on nonuniform rectangular partitions. The DMP analysis is based on a simplified formulation of the WG involving only the approximating functions defined on the boundary of each element. The simplified weak Galerkin (SWG) method has a reduced computational complexity over the usual WG, and indeed provides a discretization scheme different from the WG when the reaction terms are present. An application of the SWG on uniform rectangular partitions yields some 5‐ and 7‐point finite difference schemes for the second order elliptic equation. Numerical experiments are presented to verify the DMP and the accuracy of the scheme, particularly the finite difference scheme.