A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions. Issue 3 (18th November 2019)

• Record Type: Journal Article
• Authors: Liu, Yujie; Wang, Junping
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 3(2020)
• Page Start: 552
• Page End: 578
• Publication Date: 2019-11-18
• Subjects: discrete maximum principle -- finite difference method -- finite element method -- second order elliptic equations -- simplified weak Galerkin; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22440
• Languages: English
• ISSNs: 0749-159X

Abstract

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.