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Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations
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
doi:10.1016/j.cam.2009.10.013
fatcat:pae5tnhvwbdupggg7xqg2d76my