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The Weak Galerkin Method for Elliptic Eigenvalue Problems

The Weak Galerkin Method for Elliptic Eigenvalue Problems
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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.

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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.

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