Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 607–627
Abstract
The authors formulated in [32] a multipoint flux mixed finite element method that reduces to a cell-centered pressure system on general quadrilaterals and hexahedra for elliptic equations arising in subsurface flow problems. In addition they showed that a special quadrature rule yields $\mathcal{O}(h)$ convergence for face fluxes on distorted hexahedra. Here a first order local velocity postprocessing procedure using these face fluxes is developed and analyzed. The algorithm involves solving a 3$\times$3 system on each element and utilizes an enhanced mixed finite element space introduced by Falk, Gatto, and Monk [18]. Computational results verifying the theory are demonstrated.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-649
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 607–627
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: mixed finite element multipoint flux approximation cell-centered finite difference mimetic finite difference full tensor coefficient quadrilaterals hexahedra postprocessing.