Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems |
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Authors: | Guoqing Zhu Shaochun Chen |
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Institution: | a School of Science, Beijing Institute of Technology, Beijing 100081, PR China b Department of Mathematics, Zhengzhou University, Zhengzhou 450052, PR 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 singular 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. |
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Keywords: | 65N15 |
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