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Advanced Numerical Methods in the Mathematical Sciences

Lin Mu, Michigan State University
Weak Galerkin Finite Element Methods and Numerical Applications

Abstract

Weak Galerkin finite element methods are new numerical methods for solving partial differential equations (PDEs) that were first introduced by Wang and Ye for solving general second-order elliptic PDEs. The differential operators in PDEs are replaced by their weak forms through integration by parts, which endows high flexibility for handling complex geometries, interface discontinuities, and solution singularities. This new method is a discontinuous finite element algorithm, which is parameter free, symmetric, and absolutely stable. Furthermore, through the Schur-complement technique, an effective implementation of the weak Galerkin is developed as a linear system involving unknowns only associated with element boundaries. In this talk, several numerical applications of weak Galerkin methods will be discussed.