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Adaptive finite element methods for the Laplace eigenvalue problem
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R. H. W. Hoppe
Published/Copyright:
December 20, 2010
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.
Received: 2009-11-15
Revised: 2010-08-22
Published Online: 2010-12-20
Published in Print: 2010-December
© de Gruyter 2010
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Articles in the same Issue
- A polynomial chaos approach to stochastic variational inequalities
- On the efficient convolution with the Newton potential
- Adaptive finite element methods for the Laplace eigenvalue problem
- Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error
Keywords for this article
adaptive finite element methods;
a posteriori error analysis;
Laplace eigenvalue problem
Articles in the same Issue
- A polynomial chaos approach to stochastic variational inequalities
- On the efficient convolution with the Newton potential
- Adaptive finite element methods for the Laplace eigenvalue problem
- Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error
