FINITE-ELEMENT APPROXIMATION OF THE TRANSPORT OF REACTIVE SOLUTES IN POROUS-MEDIA .2. ERROR-ESTIMATES FOR EQUILIBRIUM ADSORPTION PROCESSES

In this paper we analyze a fully practical piecewise linear finite ele ment approximation involving numerical integration, backward Euler tim e discretization, and possibly regularization and relaxation of the fo llowing degenerate parabolic equation arising in a model of reactive s olute transport in porous media: find u(x, t) such that partial deriva tive(t)u + partial derivative(t)[phi(u)] - Delta u = f in Omega x (0, T], u = 0 on partial derivative Omega x (0, T] u(., 0) = g(.) in Omega for known data Omega subset of R(d), 1 less than or equal to d less t han or equal to 3, f, g, and a monotonically increasing phi is an elem ent of C-0(R) boolean AND C-1(-infinity, 0] boolean OR (0, infinity) s atisfying phi(0) = 0, which is only locally Holder continuous with exp onent p is an element of (0, 1) at the origin; e.g., phi(s) = [s](+)(p ). This lack of Lipschitz continuity at the origin limits the regulari ty of the unique solution u and leads to difficulties in the finite el ement error analysis.