A mimetic Green element method. (February 2019)

• Record Type: Journal Article
• Authors: Rao, Xiang; Cheng, Linsong; Cao, Renyi; Zhang, Xiao; Dai, Dan
• Is Part Of: Engineering analysis with boundary elements. Volume 99(2019)
• Page Start: 206
• Page End: 221
• Publication Date: 2019-02
• Subjects: Green element method -- Mimetic finite difference method -- Boundary element method -- Finite difference method -- Finite element method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2018.12.004
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Green element method (GEM) is a numerical approach that combines boundary element method (BEM) and finite element method (FEM), which is effective to solve many physical problems, such as diffusion equation, heat transfer equation, etc. This paper proposes a novel GEM named mimetic GEM, which utilizes discrete flux operator derived from mimetic FDM to approximate boundary integral of the product of fundamental solution and edge-normal flux in GEM. Proposed mimetic GEM is indeed a novel numerical method mixing the ideas of BEM, FEM, and mimetic FDM, which The method synthesizes some typical advantages of traditional numerical methods, that has a semi-analytical accuracy same as BEM. The method can be adaptive to unstructured grid same as FEM, and has a good convergence same as FDM.