Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations

Authors:
Guanghua Gao;Tongke Wang
Affiliations:
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, PR China;School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 11
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Abstract

In this paper, a cubic superconvergent finite volume element method based on optimal stress points is presented for one-dimensional elliptic and parabolic equations. For elliptic problem, it is proved that the method has optimal third order accuracy with respect to H^1 norm and fourth order accuracy with respect to L^2 norm. We also obtain that the scheme has fourth order superconvergence for derivatives at optimal stress points. For parabolic problem, the scheme is given and error estimate is obtained with respect to L^2 norm. Finally, numerical examples are provided to show the effectiveness of the method.