Abstract:

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.

个人简介：

张然, 理学博士，吉林大学数学学院教授，博士生导师。主要从事非标准有限元方法、多尺度分析及应用等课题研究。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》、《J. Comput. Phys.》、《IMA J Numerical Analysis》等杂志上发表学术论文60余篇。