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数学学院、所系列学术报告(801场): 美国科罗拉多州立大学 刘江国教授

发表于: 2018-06-22 15:16  点击:

报告题目:New and Renovated Finite Elements on Quadrilaterals

报告人: 刘江国教授  美国科罗拉多州立大学

报告时间:2018622日下午3:00

报告地点:数学楼202研究室

报告摘要:This talk presents some new and renovated finite elements that aim at solving Darcy, elasticity, and poroelasticity.  The novel weak Galerkin (WG) finite element methods (FEMs) use degree k(>=0) polynomials in element interiors and on edges separately for approximating the primal variable (pressure).  The discrete weak gradients of these weak basis functions are established in the rbogast-Correa spaces, which are improvements of the classical Raviart-Thomas spaces.  These discrete weak gradients are then used to approximate the classical gradient in the

variational form.  These new FEMs do not use any nonphysical penalty but are locally conservative and produce continuous normal fluxes. Furthermore, these new methods have optimal-order convergence in pressure, velocity, normal flux, and div of velocity.  The Bernardi-Raugel elements, originally designed For Stokes flow, can be re-used for elasticity, after incorporation of the techniques of reduced integration.  These methods will be combined to solve poroelasticity.  Numerical examples will be presented to illustrate these ideas.