Smoothing and newton's method for a discontinuous variational equation of stefan type*

Abstract

An important way to treat discontinuous variational equations consists in its embedding into a family of continuous ones. In the present paper for this purpose a smooth penalty technique is applied. Convergence bounds are derived for the approximation of the original solution by solutions of the generated smoothed problems. The focus of the papers is to analyze a semi-discretization via Rothe's method and to establish Convergence bounds for Newton's method applied to it depending on discretization and smoothing parameters. The subproblems at each time level can be considered as nonsmooth convex variational problems of obstacle type