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.

Biography:

Dr. Ran Zhang is a Mathematics Professor at Jilin University.  Zhang’s primary research interests include non-standard finite element methods, multi-scale analysis and applications. Published more than 60 academic papers in journals including SIAM J Numerical Analysis, Mathematics of Computation, SIAM J Scientific Computing, J. Comput. Phys. etc.