摘       要：Weak Galerkin finite element methods are new numerical methods for solving partial differential equations that were first introduced by Wang and Ye for solving general second order elliptic partial differ- ential equations (PDEs). The differential operators in PDEs are replaced by their weak forms through the 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 a linear system involving unknowns only associated with element boundaries. In this talk, several numerical applications of weak Galerkin methods will be discussed.