Int. J. Numer. Anal. Mod., 3 (2006), pp. 348-360.


A symmetric finite volume element scheme on quadrilateral grid and superconvergence

Shi Shu 1, Haiyaun Yu 1, Yunqing Huang 1, Cunyun Nie 1

1 Institute for Computational and Applied Mathematics, Xiangtan University, Hunan, P.R. China, 411105

Received by the editors August 1, 2004 and, in revised form, March 22, 2005
Abstract

A symmetric finite volume element scheme on quadrilateral grids is established for a class of elliptic problems. The asymptotic error expansion of finite volume element approximation is obtained under rectangle grids, which in turn yields the error estimates and superconvergence of the averaged derivatives. Numerical examples confirm our theoretical analysis.

AMS subject classifications: 65N30, 65F10
Key words: quadrilateral grids; symmetric finite volume schemes; asymptotic error expansion; superconvergence
Email: huangyq@xtu.edu.cn (Y. Huang), shushi@xtu.edu.cn (S. Shu)
 

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