Fully discrete mixed finite element approximations for non-Darcy flows in porous media

Comparison of Binomial and Power Equations in Radial Non-Darcy Flows in Coarse Porous Media

Analysis of non-laminar flows in coarse alluvial beds has a wide range of applications in various civil engineering, oil and gas, and geology problems. Darcy equation is not valid to analyze transient and turbulent flows, so non-linear equations should be applied. Non-linear equations are classified into power and binomial equations. Binomial equation is more accurate in a wide range of velocit...

Finite Volume Element Approximations of Nonlocal Reactive Flows in Porous Media

In this paper we study nite volume element approximations for two dimensional parabolic integro di erential equations arising in modeling of nonlocal reactive ows in porous media These type of ows are also called NonFickian ows with mixing length growth For simplicity we only consider linear nite volume element methods although higher order volume elements can be considered as well under this f...

Well-Conditioned Iterative Schemes for Mixed Finite-Element Models of Porous-Media Flows

Mixed finite-element methods are attractive for modeling flows in porous media since they can yield pressures and velocities having comparable accuracy. In solving the resulting discrete equations, however, poor matrix conditioning can arise both from spatial heterogeneity in the medium and from the fine grids needed to resolve that heterogeneity. This paper presents two iterative schemes that ...

Sharp L2-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media

Sharp L-error Estimates and Superconvergence of Mixed Finite Element Methods for Non-fickian Flows in Porous Media∗

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...