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

Guanghua Gao, Tongke Wang
2010 Journal of Computational and Applied Mathematics  
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
more » ... btained with respect to L 2 norm. Finally, numerical examples are provided to show the effectiveness of the method.
doi:10.1016/j.cam.2009.10.013 fatcat:pae5tnhvwbdupggg7xqg2d76my