Adaptive finite element methods for the Laplace eigenvalue problem

R. H. W. Hoppe

doi:10.1515/JNUM.2010.014

Adaptive finite element methods for the Laplace eigenvalue problem

2010-01-01

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DOI：10.1515/JNUM.2010.014

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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.

Keyword:

adaptive finite element methods

a posteriori error analysis

Laplace eigenvalue problem

Adaptive finite element methods for the Laplace eigenvalue problem

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