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 approximation by continuous piecewise linears in space of the following problem: Given Ohm subset of R-d; 1 less than or equal to d less than or equal 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 the spatial differential operator is uniformly elliptic, but phi is an element of C-0 (R) boolean AND C-1 (-infinity, 0] boolean OR (0, infinity) is a monotonically increasing function satisfying phi(0) = 0, which 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 bounds which improve on those in the literature.