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Volume 5, Issue 1
Error Analysis of Local Refinements of Polygonal Domains

Wei-Nan E, Hong-Ci Huang & Wei-Min Han

J. Comp. Math., 5 (1987), pp. 89-94.

Published online: 1987-05

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  • Abstract

This paper gives a thorough analysis of the local refinement method on plane polygonal domains with special attention to the treatment of reentrant corner. Convergence rates of the finite element method under various norms are derived via a systematic treatment of the interpolation theory in weighted Sobolev spaces. It is proved that by refining the mesh suitably, the finite element approximations for problems with singularities achieve the same convergence rates as those for smooth solutions.

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@Article{JCM-5-89, author = {Wei-Nan E, Hong-Ci Huang and Wei-Min Han}, title = {Error Analysis of Local Refinements of Polygonal Domains}, journal = {Journal of Computational Mathematics}, year = {1987}, volume = {5}, number = {1}, pages = {89--94}, abstract = {

This paper gives a thorough analysis of the local refinement method on plane polygonal domains with special attention to the treatment of reentrant corner. Convergence rates of the finite element method under various norms are derived via a systematic treatment of the interpolation theory in weighted Sobolev spaces. It is proved that by refining the mesh suitably, the finite element approximations for problems with singularities achieve the same convergence rates as those for smooth solutions.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9534.html} }
TY - JOUR T1 - Error Analysis of Local Refinements of Polygonal Domains AU - Wei-Nan E, Hong-Ci Huang & Wei-Min Han JO - Journal of Computational Mathematics VL - 1 SP - 89 EP - 94 PY - 1987 DA - 1987/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9534.html KW - AB -

This paper gives a thorough analysis of the local refinement method on plane polygonal domains with special attention to the treatment of reentrant corner. Convergence rates of the finite element method under various norms are derived via a systematic treatment of the interpolation theory in weighted Sobolev spaces. It is proved that by refining the mesh suitably, the finite element approximations for problems with singularities achieve the same convergence rates as those for smooth solutions.

Wei-Nan E, Hong-Ci Huang and Wei-Min Han. (1987). Error Analysis of Local Refinements of Polygonal Domains. Journal of Computational Mathematics. 5 (1). 89-94. doi:
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