Error estimates for multidimensional singular parabolic problems

Abstract

We consider a rather general class of singular parabolic problems; multidimensional two-phase Stefan problem and porous-medium equation involving additional nonlinearities are included. We analyze an approximation scheme consisting in a regularization procedure and discretization by means ofC °-piecewise linear finite elements in space and backward-differences in time. We prove severalL β-error estimates for the various unknowns, wherep depends on the problem. As a by-product of our technique, we obtain an optimalL 2-error estimate for enthalpy.