The Weak Galerkin Method for Elliptic Eigenvalue Problems (Communications in Computational Physics, 2019)
This article is devoted to studying the application of the weak Galerkin(WG) finite element method to the elliptic eigenvalue problem with an emphasis onobtaining lower bounds. The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions. The non-conforming finite element space ofthe WG method is the key of the lower bound property. It also makes the WG methodmore robust and flexible in solving eigenvalue problems. We demonstrate that the WGmethod can achieve arbitrary high convergence order. This is in contrast with existingnonconforming finite element methods which can provide lower bound approximations by linear finite elements. Numerical results are presented to demonstrate theefficiency and accuracy of the theoretical results.
Keywords: Weak Galerkin finite element method; elliptic eigenvalue problem; lower bounds; error estimate.