An operator Newton method for the Stefan problem based on smoothing: A local perspective (Q803432)

The enthalpy formulation for the two-phase Stefan problem leads to the equation \(\partial H(u)/\partial t-\Delta u=0\), where H is discontinuous. For numerical purposes, H is often replaced by a smooth function \(H_{\epsilon}\). The author studies the convergence to the true solution u of the solutions \(u_{\epsilon}\) of the problems \(\partial H_{\epsilon}(u_{\epsilon})/\partial t-\Delta u_{\epsilon}=R_{\epsilon}\), where \(R_{\epsilon}\) is a residual that accounts for errors in the solution of the regularized problem. The solution of the regularized equations by Newton method is also investigated.