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 framework It is proved that the derived nite element volume approximations are convergent with optimal order in H and L norm and superconvergent in a discrete H norm By examining the relationships between nite volume element and nite element approximations we prove convergence in L and W norms These results are new also for nite volume element methods for elliptic and parabolic equations c John Wiley Sons Inc