Finite volume element approximations of nonlocal reactive flows in porous media

In this article, we study finite volume element approximations for two-dime nsional parabolic integrodifferential equations, arising in the modeling of nonlocal reactive flows in porous media. These types of flows are also cal led NonFickian flows and exhibit mixing length growth. For simplicity, we c onsider only linear finite volume element methods, although higher-order vo lume elements can be considered as well under this framework. It is proved that the finite volume element approximations derived are convergent with o ptimal order in H-1- and L-2-norm and are superconvergent in a discrete H-1 -norm. By examining the relationship between finite volume element and fini te element approximations, we prove convergence in L-infinity- and W-1,W-in finity-norms. These results are also new for finite volume element methods for elliptic and parabolic equations. (C) 2000 John Wiley & Sons, Inc.