A symmetric finite volume element scheme on quadrilateral grid and superconvergence
Shi Shu 1, Haiyaun Yu 1, Yunqing Huang 1, Cunyun Nie 11 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
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: email@example.com (Y. Huang), firstname.lastname@example.org (S. Shu)