Work

Weak Galerkin Finite Element Methods on Polytopal Meshes

Year: 2015

Type: article

Abstract: This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed and why they provide reliable numerical approximations for the underlying partial differential equations. In particular, optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability, and accuracy of the WG-FEM. All the results are established for finite element partitions with polytopes that are shape regular.

Source: International Journal of Numerical Analysis and Modeling

DOI: 10.4208/ijnam.v12.n1.p31

Authors: Lin Mu, Junping Wang, Xiu Ye

Institutions: Michigan State University, U.S. National Science Foundation, Division of Mathematical Sciences, University of Arkansas at Little Rock

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Adaptive Finite Element Method for Interface Problems