Abstract:This talk will introduce a new finite element technique for partial differential equations. This new method is based on a computation of derivatives (first and second or higher order) as a generalized function or distribution for discontinuous finite element functions. In this talk, the speaker will explain the main idea of the weak Galerkin method by using a second order elliptic equation. The method will then be applied to other PDEs, such as the Stokes equations and the biharmonic equation. The talk should be accessible to graduate students as well as researchers in computational mathematics.