On the finite element approximation of the boundary control for two-phase stefan problems

Abstract

A boundary control for a two-phase Stefan problem is considered. The problem is regularized by utilizing the Yosida approximation and the Friedrichs mollifier. Next it is discretized by finite elements in space and finite differences in time. The solution of these auxiliary problems are shown to be minimizing sequences for the original problem when certain parameters approach to zero. A gradient algorithm is presented for the discretized problem. Numerical test example illustrates the efficiency of the methods.