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Volume 15, Issue 2
Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem

Jiajun Zhan, Liuqiang Zhong & Jie Peng

DOI: 10.4208/aamm.OA-2021-0257

Adv. Appl. Math. Mech., 15 (2023), pp. 450-467.

Published online: 2022-12

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  • Abstract

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretization is first established, then the corresponding well-posedness is provided by using Brouwer’s fixed point method. Some optimal priori error estimates under both DG norm and $L^2$ norm are presented, respectively. Numerical results are given to illustrate the efficiency of the proposed approach.

  • Keywords

Semilinear elliptic problem, discontinuous Galerkin method, error estimates.

  • AMS Subject Headings

65N30, 35J60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-450, author = {Zhan , JiajunZhong , Liuqiang and Peng , Jie}, title = {Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {2}, pages = {450--467}, abstract = {

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretization is first established, then the corresponding well-posedness is provided by using Brouwer’s fixed point method. Some optimal priori error estimates under both DG norm and $L^2$ norm are presented, respectively. Numerical results are given to illustrate the efficiency of the proposed approach.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0257}, url = {http://global-sci.org/intro/article_detail/aamm/21276.html} }
TY - JOUR T1 - Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem AU - Zhan , Jiajun AU - Zhong , Liuqiang AU - Peng , Jie JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 450 EP - 467 PY - 2022 DA - 2022/12 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0257 UR - https://global-sci.org/intro/article_detail/aamm/21276.html KW - Semilinear elliptic problem, discontinuous Galerkin method, error estimates. AB -

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretization is first established, then the corresponding well-posedness is provided by using Brouwer’s fixed point method. Some optimal priori error estimates under both DG norm and $L^2$ norm are presented, respectively. Numerical results are given to illustrate the efficiency of the proposed approach.

Zhan , JiajunZhong , Liuqiang and Peng , Jie. (2022). Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem. Advances in Applied Mathematics and Mechanics. 15 (2). 450-467. doi:10.4208/aamm.OA-2021-0257
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