Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:255

Article

Mu, Lin¹  Wang, Junping²  Wang, Yanqiu³  Ye, Xiu⁴ 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA

[3] Oklahoma State Univ, Dept Math, Stillwater, OK 74075 USA

[4] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

关键词: Discontinuous Galerkin;    Finite element;    Interior penalty;    Second-order elliptic equations;    Hybrid mesh;   

DOI  :  10.1016/j.cam.2013.06.003

来源: Elsevier

【 摘 要 】

This paper provides a theoretical foundation for interior penalty discontinuous Galerkin methods for second-order elliptic equations on very general polygonal or polyhedral meshes. The mesh can be composed of any polygons or polyhedra that satisfy certain shape regularity conditions characterized in a recent paper by two of the authors, Wang and Ye (2012) [11]. The usual H-1-conforming finite element methods on such meshes are either very complicated or impossible to implement in practical computation. The interior penalty discontinuous Galerkin method provides a simple and effective alternative approach which is efficient and robust. Results with such general meshes have important application in computational sciences. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free