Error bounds for the finite element approximation of a degenerate quasilinear parabolic variational inequality

In this paper, we establish some error bounds for the continuous piecewise linear finite element approximation of the following problem: Let ? be an open set in ?d, with d=1 or 2. Given T>0, p ? (1, ?), f and u0; find u ?K, where K is a closed convex subset of the Sobolev space W01, p(?), such that for any v?K {Mathematical expression} We prove error bounds in energy type norms for the fully discrete approximation using the backward Euler time discretisation. In some notable cases, these error bounds converge at the optimal rate with respect to the space discretisation, provided the solution u is sufficiently regular.