A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method

Authors

  • Wei Yang Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, P.R.China
  • Luling Cao Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, P.R.China
  • Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, P.R.China
  • Jintao Cui Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

Keywords:

Interior penalty discontinuous Galerkin method, a posteriori error estimate, adaptive finite element methods, Gauss-Seidel iterative method.

Abstract

In this paper, we develop the adaptive interior penalty discontinuous Galerkin method based on a new $a$ $posteriori$ error estimate for the second-order elliptic boundary-value problems. The new $a$ $posteriori$ error estimate is motivated from the smoothing iteration of the $m$-time Gauss-Seidel iterative method, and it is used to construct the adaptive finite element method. The efficiency and robustness of the proposed adaptive method is demonstrated by extensive numerical experiments.

Downloads

Published

2019-02-22

Issue

Vol. 16 No. 2 (2019)

Section

Articles