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

H. Blum & R. Rannacher

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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 lement 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, eleminating 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 eigenfuncitons which are globally defined quantities.

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@Article{JCM-8-321, author = {}, title = {Finite Element Eigenvalue Computation on Domains with Reentrant Coners 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 lement 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, eleminating 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 eigenfuncitons 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 Coners Using Richardson Extrapolation 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 lement 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, eleminating 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 eigenfuncitons which are globally defined quantities.
H. Blum & R. Rannacher. (1970). Finite Element Eigenvalue Computation on Domains with Reentrant Coners Using Richardson Extrapolation. Journal of Computational Mathematics. 8 (4). 321-332. doi:
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