Lowest-order Weak Galerkin Finite Element Method for Elliptic Problems on General Polygonal Meshes
报告题目：Lowest-order Weak Galerkin Finite Element Method for Elliptic Problems on General Polygonal Meshes
报告时间：2018年6月26日，星期二，上午10:00---12:00
报告地点：理科楼407
Abstract:
This talk presents the lowest-order weak Galerkin (WG) finite element method for Darcy flow or elliptic boundary value problems on general convex polygonal meshes. In this approach, constants are used in element interiors and on edges to approximate the primal variable (pressure). The discrete weak gradients of these constant basis functions are established in simple H(div)-subspaces on polygons that are explicitly constructed by using the normalized coordinates and Wachspress coordinates. These discrete weak gradients are used to approximate the classical gradient in the variational form. No penalization is needed for this new method. The method results in symmetric positive-definite sparse linear systems. It is locally mass-conservative, and produces continuous normal fluxes. The new method has optimal-order convergence in pressure (primal variable), velocity, and normal flux, when the convex polygon meshes are shape-regular.
报告人简介：
Dr. Yang got his Ph.D from University of South Carolina at 2001. He worked as a visiting assistant professor at Texas A&M University from 2002 to 2005, and started the assistant professorship at Colorado State University then. He is now a full professor of Colorado State University. His research interests include Computational Math (finite elements), Data Science (machine learning, TensorFlow), Mathematical Biology (cellular protein trafficking), Scientific Computing (flow in porous media, poroelasticity). He published more than 40 peer reviewed journal papers and was invited to give more than 50 talks and seminars in many conferences, universities and institutes around the world. He served as SIAM Central States Section President and Associate Editor for Journal of Computational and Applied Mathematics.
