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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.

  • Keywords

mixed finite element, multipoint flux approximation, cell-centered finite difference, mimetic finite difference, full tensor coefficient, quadrilaterals, hexahedra, postprocessing.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-607, author = {M. Wheeler, G. Xue and I. Yotov}, 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 AU - M. Wheeler, G. Xue & I. Yotov 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 and I. Yotov. (2012). 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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