Interior superconvergence error estimates for mixed finite element methods for second order elliptic problem |
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| Authors: | Luo Ping Liao Xiaohai |
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| Affiliation: | (1) Department of Computer Science and Technology, Tsinghua University, 100084 Beijing, China;(2) Department of Mathematics, Maryland University, USA |
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| Abstract: | The aim of this paper is to provide a local superconvergence analysis for mixed finite element methods of Poission equation. We shall prove that ifp is smooth enough in a local region  and rectangular mesh is imposed on Ω{in1}, then local superconvergence for ∥π{inh}{itu}−{itu}{inh}∥0,2,Ω{in0}, and ∥P{inh}p−p{inh}∥0,2,Ω{in0}, are expected. Thus, by post-processing operators  and  , we have obtained the following local superconvergence error estimate: ![$$||p - tilde P_{ph} ||o_1 Omega _0 || + ||u - tilde pi u_h ||o_1 Omega _o leqslant cleft[ {h^{k + 2.5} ||p||k + 4_, Omega _1 + h^{k + 1 + r - e} ||p||2 + r_, Omega } right]_, $$](/content/8143341j013236r1/10255_2007_Article_BF02669827_TeX2GIFIE4.gif) where 0≤r≤2 andk≥1. |
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| Keywords: | Local superconvergence mixed finite element Raviart-Thomas space interpolation finite element |
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