Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra

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.