Year: 2020
Author: Xiu Ye, Shangyou Zhang
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 281–296
Abstract
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [19] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous finite element method. The goal of this paper is to extend the conforming DG finite element method in [19] so that it can work on general polytopal meshes by designing weak gradient ∇$w$ appropriately. Two different conforming DG formulations on polytopal meshes are introduced which handle boundary conditions differently. Error estimates of optimal order are established for the corresponding conforming DG approximation in both a discrete $H$1 norm and the $L$2 norm. Numerical results are presented to confirm the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13651
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 2 : pp. 281–296
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Weak Galerkin discontinuous Galerkin stabilizer/penalty free finite element methods second order elliptic problem.