Superconvergence of conforming finite element for fourth‐order singularly perturbed problems of reaction diffusion type in 1D |
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| Authors: | Hailong Guo Can Huang Zhimin Zhang |
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| Institution: | 1. Department of Mathematics, Wayne State University, , Detroit, MI, 48202;2. Department of Mathematics, Michigan State University, , East Lansing, MI, 48824;3. Beijing Computational Science Research Center, , Beijing, 100084 People's Republic of China |
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| Abstract: | We consider conforming finite element approximation of fourth‐order singularly perturbed problems of reaction diffusion type. We prove superconvergence of standard C1 finite element method of degree p on a modified Shishkin mesh. In particular, a superconvergence error bound of  in a discrete energy norm is established. The error bound is uniformly valid with respect to the singular perturbation parameter ?. Numerical tests indicate that the error estimate is sharp. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 550–566, 2014 |
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| Keywords: | superconvergence fourth order singular perturbation conforming finite element reaction diffusion Shishkin mesh |
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