Superconvergent error estimates for a class of discretization methods for a coupled first-order system with discontinuous coefficients

Lithological discontinuities in a reservoir generate discontinuous coeffici ents for the first-order system of equations used in the simulation of flui d flow in porous media. Systems of conservation laws with discontinuous coe fficients also arise in many other physical applications. In this article, we present a class of discretization schemes that include variants of mixed finite element methods, finite volume element methods, and cell-centered f inite difference equations as special cases. Error estimates of the order O (h(2)) in certain discrete L-2-norms are established for both the primary i ndependent variable and its flux, even in the presence of discontinuous coe fficients in the flux term. (C) 1999 John Wiley & Sons, Inc.