The weak Galerkin finite element method for elliptic eigenvalue problems

主讲人：张然 吉林大学教授

时间：2022年5月27日15：00

地点：腾讯会议 554 959 652

举办单位：数理学院

主讲人介绍：张然，教授、博士生导师。1999年本科毕业于吉林大学数学系，2004年获得吉林大学计算数学博士学位。现任吉林大学数学学院党委书记、院长，吉林国家应用数学中心主任，吉林省运筹学会理事长等职务。主要从事非标准有限元方法及相关软件平台的开发等研究工作，在包括计算数学领域的重要期刊《SIAM J Numerical Analysis》、《Mathematics of Computation》、《SIAM J Scientific Computing》等上发表学术论文60余篇。主持及完成基金委重大研究计划重点项目等7项国家级项目，担任AMC、DCDS-B、CMR等期刊编委。

内容介绍：This talk is devoted to studying eigenvalue problem by the weak Galerkin (WG) finite element method with an emphasis on obtaining lower bounds. The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions. As such it is more robust and flexible in solving eigenvalue problems since it finds eigenvalue as a min-max of Rayleigh quotient in a larger finite element space. We demonstrate that the WG methods can achieve arbitrary high order convergence. This is in contrast with classical nonconforming finite element methods which can only provide the lower bound approximation by linear elements with only the second order convergence. We also presented the guaranteed lower bound for k=1 order polynomials and some acceleration techniques are applied to WG method.