  The eXtreme Mesh deformation approach (X-MESH) is a new paradigm to follow
sharp interfaces without remeshing and without changing the mesh topology. Even
though the mesh does not change its topology, it can follow interfaces that do
change their topology (nucleation, coalescence, splitting). To make this
possible, the key X-MESH idea is to allow elements to reach zero measure. This
permits interface relaying between nodes as well as interface annihilation and
seeding in a time continuous manner. The paper targets the Stefan phase change
model in which the interface (front) is at a given temperature. Several
examples demonstrate the capability of the approach.
