Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction–diffusion problems |
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| Authors: | Guoqing Zhu Shaochun Chen |
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| Institution: | 1. Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Republic of China;2. Department of Mathematics, Zhengzhou University, 450052 Zhengzhou, People's Republic of China |
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| Abstract: | The numerical approximation by a lower‐order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi‐optimal‐order error estimates are proved in the ε‐weighted H1‐norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in ε‐weighted H1‐norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | semisingular perturbation graded meshes finite elements error estimates |
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