Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem

Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem

Year:    2023

Author:    Jiajun Zhan, Liuqiang Zhong, Jie Peng

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0257

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 450–467

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Semilinear elliptic problem discontinuous Galerkin method error estimates.

Author Details

Jiajun Zhan

Liuqiang Zhong

Jie Peng

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