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Volume 14, Issue 2
A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms

Fuzheng Gao, Xiu Ye & Shangyou Zhang

Adv. Appl. Math. Mech., 14 (2022), pp. 299-314.

Published online: 2022-01

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  • 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.

  • Keywords

Nonhomogeneous Dirichlet boundary conditions, weak gradient, discontinuous Galerkin, stabilizer, penalty free, finite element methods, polytopal mesh.

  • AMS Subject Headings

65N15, 65N30, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-299, author = {Fuzheng and Gao and and 22042 and and Fuzheng Gao and Xiu and Ye and and 22043 and and Xiu Ye and Shangyou and Zhang and and 22044 and and Shangyou Zhang}, title = {A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0247}, url = {http://global-sci.org/intro/article_detail/aamm/20199.html} }
TY - JOUR T1 - A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms AU - Gao , Fuzheng AU - Ye , Xiu AU - Zhang , Shangyou JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 299 EP - 314 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0247 UR - https://global-sci.org/intro/article_detail/aamm/20199.html KW - Nonhomogeneous Dirichlet boundary conditions, weak gradient, discontinuous Galerkin, stabilizer, penalty free, finite element methods, polytopal mesh. AB -

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.

Fuzheng Gao, Xiu Ye & Shangyou Zhang. (2022). A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms. Advances in Applied Mathematics and Mechanics. 14 (2). 299-314. doi:10.4208/aamm.OA-2020-0247
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