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Volume 9, Issue 3
Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra

M. Wheeler, G. Xue & I. Yotov

Int. J. Numer. Anal. Mod., 9 (2012), pp. 607-627.

Published online: 2012-09

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  • 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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@Article{IJNAM-9-607, author = {}, title = {Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/649.html} }
TY - JOUR T1 - Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 607 EP - 627 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/649.html KW - mixed finite element, multipoint flux approximation, cell-centered finite difference, mimetic finite difference, full tensor coefficient, quadrilaterals, hexahedra, postprocessing. AB -

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.

M. Wheeler, G. Xue & I. Yotov. (1970). Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra. International Journal of Numerical Analysis and Modeling. 9 (3). 607-627. doi:
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