Primal-Dual Weak Galerkin FEMs for PDEs

题    目:Primal-Dual Weak Galerkin FEMs for PDEs

报告人:Dr. Chunmei Wang, Department of Mathematics, Texas State University

摘 要:In this talk, the speaker will introduce the basic ideas and a general framework for weak Galerkin (WG) methods by using the second order elliptic equation as a model problem. The speaker will then discuss a recent development of WG, known as “Primal-Dual Weak Galerkin (PD-WG)”. The essential idea of PD-WG is to interpret the numerical solutions as constrained minimization of some functionals with constraints that mimic the weak formulation of the PDEs by using the weak derivatives. The resulting Euler-Lagrange equation offers a symmetric finite element scheme involving both the primal and the dual variable (also known as the Lagrange multiplier). The primal-dual WG methods will be applied to several challenging problems for which existing methods have difficulty in applying; these problems include the second order elliptic equations in nondivergence form, Fokker-Planck equation, first order convection equations, and elliptic Cauchy problems. Finally, the speaker will introduce an abstract framework for the PD-WG method and discuss its great potential in other scientific applications.

时    间:2018年5月23日 15:00-16:00

地    点:知新楼 B座 1044