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Superconvergence of quadratic finite elements on mildly structured grids


Authors: Yunqing Huang and Jinchao Xu
Journal: Math. Comp. 77 (2008), 1253-1268
MSC (2000): Primary 65N50, 65N30
Published electronically: March 4, 2008
MathSciNet review: 2398767
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Abstract: Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution $ u_h$ is proven to be superclose to the interpolant $ u_I$ and as a result a postprocessing gradient recovery scheme for $ u_h$ can be devised. The analysis is based on a number of carefully derived identities. In addition to its own theoretical interests, the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods.


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Additional Information

Yunqing Huang
Affiliation: Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, People’s Republic of China, 411105
Email: huangyq@xtu.edu.cn

Jinchao Xu
Affiliation: Institute for Computational and Applied Mathematics, Xiangtan University, People’s Republic of China and Center for Computational Mathematics and Applications, Pennsylvania State University, USA
Email: xu@math.psu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02051-6
Keywords: Superconvergence, gradient recovery, a posteriori error estimates
Received by editor(s): February 2, 2006
Received by editor(s) in revised form: March 2, 2007
Published electronically: March 4, 2008
Additional Notes: The work of the first author was supported in part by the NSFC for Distinguished Young Scholars (10625106) and the National Basic Research Program of China under the grant 2005CB321701
The second author was supported in part by the Furong Scholar Program of Hunan Province through Xiangtan University
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.