A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh. Issue 3 (21st November 2019)

• Record Type: Journal Article
• Authors: Cui, Jintao; Gao, Fuzheng; Sun, Zhengjia; Zhu, Peng
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 3(2020)
• Page Start: 601
• Page End: 616
• Publication Date: 2019-11-21
• Subjects: a posteriori error estimate -- discontinuous Galerkin methods -- polytopal mesh -- second‐order elliptic problems; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22443
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this work, we derive a posteriori error estimates for discontinuous Galerkin finite element method on polytopal mesh. We construct a reliable and efficient a posteriori error estimator on general polygonal or polyhedral meshes. An adaptive algorithm based on the error estimator and DG method is proposed to solve a variety of test problems. Numerical experiments are performed to illustrate the effectiveness of the algorithm.