A qualocation method for a unidimensional single phase semilinear Stefan problem

Based on straightening the free boundary, a qualocation method is proposed and analysed for a single phase unidimensional Stefan problem. This method may be considered as a discrete version of the H-1-Galerkin method in which the discretization is achieved by approximating the integrals by a composite Gauss quadrature rule. Optimal error estimates are derived in L-infinity(W-j,W-infinity), j = 0, 1, and L-infinity(H-j), j = 0, 1, 2, norms for a semidiscrete scheme without any quasi-uniformity assumption on the finite element mesh