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 - <p style="text-align: justify;">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.</p>