AN IMPROVED ERROR BOUND FOR A LAGRANGE-GALERKIN METHOD FOR CONTAMINANT TRANSPORT WITH NON-LIPSCHITZIAN ADSORPTION-KINETICS

In this paper we consider the Lagrange-Galerkin finite element approxi mation by continuous piecewise linears in space of the following probl em: Given Ohm subset of R-d; 1 less than or equal to d less than or eq ual to 3, find u(x, t) and v(x, t) such that partial derivative(t)u partial derivative(t)upsilon - <(del)under bar>. ((D) double under bar <(del)under bar>u) + (q) under bar.<(del)under bar>u = f in Ohm x (0; T], partial derivative(t)upsilon = k(phi(u) - upsilon) in Omega x (0; T], u((u) under bar, 0) = g(1) ((x) under bar); upsilon((x) under bar, 0) = g(2)((x) under bar) For All (x) under bar is an element of Omega , with periodic boundary conditions. Here k is an element of R+ and th e spatial differential operator is uniformly elliptic, but phi is an e lement of C-0 (R) boolean AND C-1 (-infinity, 0] boolean OR (0, infini ty) is a monotonically increasing function satisfying phi(0) = 0, whic h is only locally Holder continuous, with exponent p is an element of (0, 1) at the origin; e.g., phi(s) := [s](+)(p). We obtain error bound s which improve on those in the literature.