A globally convergent multi-grid algorithm for moving boundary problems of two-phase Stefan type
Ronald H. W. Hoppe · IMA Journal of Numerical Analysis · 1993
In this paper we deal with the numerical solution of moving boundary problems of two-phase Stefan type. Based on an implicit discretization in time and the use of continuous, piecewise linear finite elements in the space variables with respect to the weak formulation of the problem, a globally convergent multi-grid algorithm is developed. That algorithm strongly relies on the variational characterization of the fully discretized problem as the unconstrained minimization of a subdifferentiable convex objective functional. Numerical results indicate a significant improvement in efficiency compared with previous multi-grid approaches.