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Markus Berndt, Konstantin Lipnikov, Mikhail Shashkov, Mary F. Wheeler and Ivan Yotov, "Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals", SIAM J. Numer. Anal., vol. 43, no. 4, pp. 1728-1749, 2005
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Abstract

Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar product in the velocity space. The theoretical results are confirmed by numerical experiments.

BibTeX Entry

@article{berndt-2004-superconvergence,
author = {Markus Berndt and Konstantin Lipnikov and Mikhail Shashkov and Mary F. Wheeler and Ivan Yotov},
title = {Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals},
year = {2005},
urlpdf = {http://math.lanl.gov/~berndt/Papers/superFlux.pdf},
urlps = {http://math.lanl.gov/~berndt/Papers/superFlux.ps},
journal = {SIAM J. Numer. Anal.},
volume = {43},
number = {4},
pages = {1728-1749}
}