Speaker: Chunmei Wang, Assistant Professor,Department of Mathematics, Texas State University, USA
Date: May 23, 2018
Time: 3:00 p.m.- 4:00 p.m.
Location: 1044 Lecture Hall, Block B, Zhixin Building, Central Campus
Sponsor: the School of Mathematics
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.
Dr. Chunmei Wang received her Ph.D.in computational mathematics from the Nanjing Normal University in China in 2014. Her research interests fall under the broad heading of numerical methods and scientific computing for problems in science and engineering governed by partial differential equations. Her research is interdisciplinary and addresses modeling and computation of applied problems in science and engineering. She has devised new finite element methods and established the corresponding convergence analysis for (1) linear hyperbolic equations, (2) elliptic Cauchy problems, (3) second order elliptic equations in nondivergence form, (4) Maxwell's equation, (5) linear elasticity and elastic interface problems, (6) div-curl systems, and (7) biharmonic equations.
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Edited by Xing Chenyang, Song Yijun