报告一
时间：2017年5月26日上午10:00
地点：数学中心813室
报告人：Jiangguo Liu, Colorado State University (USA)
题目："New Results of Weak Galerkin Finite Element Methods for Partial
Differential Equations"
摘要：In this talk, we present new ideas of weak Galerkin (WG) finite element
methods for solving the Darcy and elasticity equations. Given a mesh, the
WG methodology sets basis functions in element interiors and edges/faces
and establishes (through integration by parts) discrete weak gradient or
divergence or curl in certain spaces that have desired approximation
capacity. The WG approach offers also nice properties, e.g., local mass
conservation and flux normal continuity for Darcy flow and locking-free
for elasticity.
For the Darcy equation in 2-dim, we develop the lowest order WG finite
element method that utilizes constant approximants for pressure but
specifies their discrete weak gradients in Raviart-Thomas spaces. This
particular method treats triangular, rectangular, and quadrilateral meshes
in a unified approach and attains optimal-order convergence in pressure,
velocity, and flux.
Similarly, constant vector approximants can be used in element interiors
and edges/faces for solving the linear elasticity equation in 2-dim or
3-dim, whereas first order accuracy is obtained for displacement, stress,
and dilation.
报告二
时间：2017年5月27日上午10:00
地点：数学中心813室
报告人：Jiangguo Liu, Colorado State University (USA）
报告摘要：Short Bio:
Jiangguo Liu earned his Ph.D. in Mathematics from University of South
Carolina (USA) in 2001. He joined Colorado State University (USA) in
2005, where he is currently a Professor of Mathematics. His research
interests are mathematical biology, numerical analysis, and scientific
computing. He has published 40 research papers in various journals
including Journal of Computational Physics and SIAM Journal on Numerical
Analysis. His research has been supported by US National Science
Foundation. Currently he serves as an Associate Editor for Journal of
Computational and Applied Mathematics and SIAM Central States Section
President.