QUASI-NORM ERROR-BOUNDS FOR THE FINITE-ELEMENT APPROXIMATION OF SOME DEGENERATE QUASI-LINEAR ELLIPTIC-EQUATIONS AND VARIATIONAL-INEQUALITIES

In this paper energy type error bounds are established for the finite element approximation of the following variational inequality problem: Let K be a closed convex set in the Sobolev space W0(1.rho)(OMEGA) wi th rho an-element-of (1, infinity), where OMEGA is an open set in R(d) (d = 1 or 2). Given f, find u is-an-element-of K such that for any up silon is-an-element-of K integral(OMEGA) k(x, \Delu\) Delu(x).Del(upsi lon(x) - u(x))dx greater-than-or-equal-to integral(OMEGA) f(x)(upsilon (x) - u(x))dx, where k is-an-element-of C(OMEGA x (0, infinity)) is a given nonnegative function with k(., t)t strictly increasing for t gre ater-than-or-equal-to 0, but possibly degenerate. In some notable case s these error bounds converge at the optimal approximation rate provid ed the solution u is sufficiently smooth.