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 - <p style="text-align: justify;">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.</p>