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Convergence and superconvergence analysis of finite element methods on graded meshes for singularly and semisingularly perturbed reaction–diffusion problems

✍ Scribed by Guoqing Zhu; Shaochun Chen

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
571 KB
Volume
220
Category
Article
ISSN
0377-0427

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✦ Synopsis

The bilinear finite element methods on appropriately graded meshes are considered both for solving singular and semisingular perturbation problems. In each case, the quasi-optimal order error estimates are proved in the -weighted H 1 -norm uniformly in singular perturbation parameter , up to a logarithmic factor. By using the interpolation postprocessing technique, the global superconvergent error estimates in -weighted H 1 -norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis.

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