A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms

A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms

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.

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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

Fuzheng Gao

Xiu Ye

Shangyou Zhang

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