Adaptive finite element methods for the Laplace eigenvalue problem

R. H. W. Hoppe; H. Wu; Z. Zhang

doi:10.1515/jnum.2010.014

Published by De Gruyter December 20, 2010

Adaptive finite element methods for the Laplace eigenvalue problem

R. H. W. Hoppe , H. Wu and Z. Zhang

From the journal Journal of Numerical Mathematics

https://doi.org/10.1515/jnum.2010.014

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Abstract

We consider an adaptive finite element method (AFEM) for the Laplace eigenvalue problem in bounded polygonal or polyhedral domains. We provide an a posteriori error analysis based on a residual type estimator which consists of element and face residuals. The a posteriori error analysis further involves an oscillation term. We prove a reduction in the energy norm of the discretization error and the oscillation term. Numerical results are given illustrating the performance of the AFEM.

Keywords:: adaptive finite element methods; a posteriori error analysis; Laplace eigenvalue problem

Received: 2009-11-15

Revised: 2010-08-22

Published Online: 2010-12-20

Published in Print: 2010-December

Adaptive finite element methods for the Laplace eigenvalue problem

Abstract

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