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Volume 8, Issue 4
Finite Element Eigenvalue Computation on Domains with Reentrant Corners Using Richardson Extrapolation

H. Blum & R. Rannacher

J. Comp. Math., 8 (1990), pp. 321-332.

Published online: 1990-08

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  • Abstract

In the presence of reentrant corners or changing boundary conditions, standard finite element schemes have only a reduced order of accuracy even at interior nodal points. This pollution effect can be completely described in terms of asymptotic expansions of the error with respect to certain fractional powers of the mesh size. Hence, eliminating the leading pollution terms by Richardson extrapolation may locally increase the accuracy of the scheme. It is shown here that this approach also gives improved approximations for eigenvalues and eigenfunctions which are globally defined quantities.

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@Article{JCM-8-321, author = {H. Blum and R. Rannacher}, title = {Finite Element Eigenvalue Computation on Domains with Reentrant Corners Using Richardson Extrapolation}, journal = {Journal of Computational Mathematics}, year = {1990}, volume = {8}, number = {4}, pages = {321--332}, abstract = {

In the presence of reentrant corners or changing boundary conditions, standard finite element schemes have only a reduced order of accuracy even at interior nodal points. This pollution effect can be completely described in terms of asymptotic expansions of the error with respect to certain fractional powers of the mesh size. Hence, eliminating the leading pollution terms by Richardson extrapolation may locally increase the accuracy of the scheme. It is shown here that this approach also gives improved approximations for eigenvalues and eigenfunctions which are globally defined quantities.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9444.html} }
TY - JOUR T1 - Finite Element Eigenvalue Computation on Domains with Reentrant Corners Using Richardson Extrapolation AU - H. Blum & R. Rannacher JO - Journal of Computational Mathematics VL - 4 SP - 321 EP - 332 PY - 1990 DA - 1990/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9444.html KW - AB -

In the presence of reentrant corners or changing boundary conditions, standard finite element schemes have only a reduced order of accuracy even at interior nodal points. This pollution effect can be completely described in terms of asymptotic expansions of the error with respect to certain fractional powers of the mesh size. Hence, eliminating the leading pollution terms by Richardson extrapolation may locally increase the accuracy of the scheme. It is shown here that this approach also gives improved approximations for eigenvalues and eigenfunctions which are globally defined quantities.

H. Blum and R. Rannacher. (1990). Finite Element Eigenvalue Computation on Domains with Reentrant Corners Using Richardson Extrapolation. Journal of Computational Mathematics. 8 (4). 321-332. doi:
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