Abstract

A new method for solving parabolic problems with the finite element method is presented. A standard approximation id enriched with local functionsin order to capture highly variable, moving solutions. To this end, a projection technique is developed for transferring solution in formation between global and local approximations. The method is particularly well suited for studying problems with moving materials interfaces, in particular phase change problems. Several one dimensional benchmark problem and two-dimensional applications are presented to illustrate the overall accuracy and utility of the new method.