Numerical analysis with the phase field equations for the Stefan   problems
  Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which complicated movements or changes are needed. More precisely, we analyze the dissolution and/or precipitation without the unknown velocity functions like the Navier-Stokes equations numerically. 
Jun-ichi Koga
math.AP cond-mat.stat-mech math.NA