A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions |
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Authors: | Yujie Liu Junping Wang |
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Affiliation: | 1. Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, China;2. Division of Mathematical Sciences, National Science Foundation, Alexandria, Virginia |
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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. |
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Keywords: | discrete maximum principle finite difference method finite element method second order elliptic equations simplified weak Galerkin |
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