Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 1 : pp. 160–191
Abstract
This article is devoted to studying the application of the weak Galerkin (WG) finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds. The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions. The non-conforming finite element space of the WG method is the key of the lower bound property. It also makes the WG method more robust and flexible in solving eigenvalue problems. We demonstrate that the WG method can achieve arbitrary high convergence order. This is in contrast with existing nonconforming finite element methods which can provide lower bound approximations by linear finite elements. Numerical results are presented to demonstrate the efficiency and accuracy of the theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0201
Communications in Computational Physics, Vol. 26 (2019), Iss. 1 : pp. 160–191
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Weak Galerkin finite element method elliptic eigenvalue problem lower bounds error estimate.