Year: 2022
Author: Fuzheng Gao, Xiu Ye, Shangyou Zhang
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 299–314
Abstract
A conforming discontinuous Galerkin finite element method was introduced by Ye and Zhang, on simplicial meshes and on polytopal meshes, which has the flexibility of using discontinuous approximation and an ultra simple formulation. The main goal of this paper is to improve the above discontinuous Galerkin finite element method so that it can handle nonhomogeneous Dirichlet boundary conditions effectively. In addition, the method has been generalized in terms of approximation of the weak gradient. Error estimates of optimal order are established for the corresponding discontinuous finite element approximation in both a discrete $H^1$ norm and the $L^2$ norm. Numerical results are presented to confirm the theory.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0247
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 299–314
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Nonhomogeneous Dirichlet boundary conditions weak gradient discontinuous Galerkin stabilizer penalty free finite element methods polytopal mesh.
Author Details
-
A modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes
Wang, Chunmei | Ye, Xiu | Zhang, ShangyouJournal of Computational and Applied Mathematics, Vol. 448 (2024), Iss. P.115918
https://doi.org/10.1016/j.cam.2024.115918 [Citations: 0] -
Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes
Ye, Xiu | Zhang, ShangyouCommunications on Applied Mathematics and Computation, Vol. (2023), Iss.
https://doi.org/10.1007/s42967-023-00330-5 [Citations: 0]