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Some superconvergence results for the covolume method for elliptic problems

✍ Scribed by Huang, Jianguo ;Li, Likang

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
109 KB
Volume
17
Category
Article
ISSN
1069-8299

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✦ Synopsis

Abstract

In this paper, we attempt to give analysis of the covolume method for solving general self‐adjoint elliptic problems. We first present some useful superconvergence results for the deviation between the solution of the covolume method and the solution of the induced finite element method, in the energy norm and maximum norm, respectively. With these results, we then reproduce the maximum norm estimates obtained by Chou and Li for the covolume method easily. Furthermore, based on the covolume method, we propose a high‐accuracy algorithm for solving general self‐adjoint elliptic problems. Compared with the original covolume method, the computation work of the new algorithm is increased slightly, but the approximate error is improved remarkably. Copyright Β© 2001 John Wiley & Sons, Ltd.

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