a variational inequality approach for one dimensional stefan problem

In this paper, we develop a numerical method to solve a famous free boundary pde called the one dimensional stefan problem.first, we rewrite the pde as a variational inequality problem (vip). using the linear finite element method, we discretize the variational inequality and achieve a linear complementarity problem (lcp). we present some existence and uniqueness theorems for solutions of the variational inequalities and free boundary problems. finally we solve the lcp numerically by applying a modification of the active set strategy.