| Article ID: | iaor20141992 |
| Volume: | 271 |
| Start Page Number: | 319 |
| End Page Number: | 327 |
| Publication Date: | Dec 2014 |
| Journal: | Journal of Computational and Applied Mathematics |
| Authors: | Wang X, Malluwawadu N S, Gao F, McMillan T C |
| Keywords: | Poisson's equation, partial differential equations (PDE) |
In this paper we introduce a new discrete weak gradient operator and a new weak Galerkin (WG) finite element method for second order Poisson equations based on this new operator. This newly defined discrete weak gradient operator allows us to use a single stabilizer which is similar to the one used in the discontinuous Galerkin (DG) methods without having to worry about choosing a sufficiently large parameter. In addition, we will establish the optimal convergence rates and validate the results with numerical examples.