Effective implementation of the weak Galerkin finite element methods for the biharmonic equation. (15th September 2017)

• Record Type: Journal Article
• Authors: Mu, Lin; Wang, Junping; Ye, Xiu
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 6(2017)
• Page Start: 1215
• Page End: 1222
• Publication Date: 2017-09-15
• Subjects: Weak Galerkin -- Finite element methods -- Weak Laplacian -- Biharmonic equations -- Polyhedral meshes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.06.002
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The weak Galerkin (WG) methods have been introduced in Mu et al. (2013, 2014), [14] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size. In fact, this reduced global system is equivalent to the Schur complements of the WG methods. The unknowns of the Schur complement of the WG method are those defined on the element boundaries. The equivalence of the WG method and its Schur complement is established. The numerical results demonstrate the effectiveness of this new implementation technique.