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Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error
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R. Rannacher
Published/Copyright:
December 20, 2010
Abstract
This paper develops a combined a posteriori analysis for the discretization and iteration errors in the solution of elliptic eigenvalue problems by the finite element method. The emphasis is on the iterative solution of the discretized eigenvalue problem by a Krylov-space method. The underlying theoretical framework is that of the Dual Weighted Residual (DWR) method for goal-oriented error estimation. On the basis of computable a posteriori error estimates the algebraic iteration can be adjusted to the discretization within a successive mesh adaptation process. The functionality of the proposed method is demonstrated by numerical examples.
Keywords:: eigenvalue problems; finite element method; mesh adaptation; DWR method; iteration error; stopping criteria
Received: 2010-10-08
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
eigenvalue problems;
finite element method;
mesh adaptation;
DWR method;
iteration error;
stopping criteria
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
