Adaptive Method for the Stefan Problem and its Application to Endoglacial Conduits

摘要

This paper concerns an adaptive finite element method for the Stefan one phase problem. We derive a parabolic variational inequality using the Duvaut transformation [1]. In each time step we consider an adaptive algorithm based on a combination of the Uzawa method associated with the corresponding multivalued operator and a convergent adaptive method for the linear problem. We justify the convergence of the method. As an application we model an endoglacial conduit in which a phase change phenomena takes place.