This article introduces a particular weak Galerkin (WG) element on rectangular/cuboid partitions that uses th order polynomial for weak finite element functions and th order polynomials for weak derivatives. This WG element is highly accurate with convergence two orders higher than the optimal order in an energy norm and the norm. The superconvergence is verified analytically and numerically. Furthermore, the usual stabilizer in the standard weak Galerkin formulation is no longer needed for this element.
A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions
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.
more » « less- NSF-PAR ID:
- 10458172
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Numerical Methods for Partial Differential Equations
- Volume:
- 36
- Issue:
- 3
- ISSN:
- 0749-159X
- Page Range / eLocation ID:
- p. 552-578
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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