3RD ORDER ACCURATE DISCONTINUOUS FINITE-ELEMENT METHOD FOR THE ONE-DIMENSIONAL STEFAN PROBLEM

A third order accurate method is proposed for the numerical solution of the one-dimensional Stefan problem. It provides approximations which are continuous with respect to the space-variable x, but which admit discontinuities with respect to the time variable t at each time step. The discretization is based on biquadratic finite elements in the plane (x, t). This method is specially appropriate for the computation of solutions which admit singularities at the initial time or on the boundary. Numerical experiments are described. © 1979.