An Oscillation-Free Adaptive FEM For Symmetric Eigenvalue Problems
Please always quote using this URN:urn:nbn:de:0296-matheon-4915
- A refined a posteriori error analysis for symmetric eigenvalue problems and the convergence of the first-order adaptive finite element method (AFEM) is presented. The $H^1$ stability of the $L^2$ projection provides reliability and efficiency of the edge-contribution of standard residual-based error estimators for $P_1$ finite element methods. In fact, the volume contributions and even oscillations can be omitted for Courant finite element methods. This allows for a refined averaging scheme and so improves [Dong Mao, Lihua Shen and Aihui Zhou, Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates, Advanced in Computational Mathematics, 2006, 25: 135-160]. The proposed AFEM monitors the edge-contributions in a bulk criterion and so enables a contraction property up to higher-order terms and global convergence. Numerical experiments exploit the remaining $L^2$ error contributions and confirm our theoretical findings. The averaging schemes show a high accuracy and the AFEM leads to optimal empirical convergence rates.
Author: | Carsten Carstensen, Joscha Gedicke |
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URN: | urn:nbn:de:0296-matheon-4915 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/03/14 |
Release Date: | 2008/03/14 |
Tag: | |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement | |
Preprint Number: | 489 |