Summary of the algorithm

We suppose that the fields at time step are known: temperature, position of the interface. The algorithm is as follows:

1. We calculate the velocity of the interface using (26).
2. We predict the position of the interface using (34).
3. We set up the set of the shape and test functions with this position of the interface.

4. 1. We initialize the values for the LATIN.
   2. We calculate the values correspond to the local step of the LATIN.
   3. We build the mass and stiffness matrices and the right hand side from (44)
      • Mass matrix:
        
        

      • Stiffness matrix:
        
        

      • Right Hand Side:
        
        
        with and , where and are the composante of and on which is the shape function of time step .
   4. We then solve the given system .
   5. We then measure the distance between the both elements ( on and ). If this distance is inferior to the tolerance, we go to the next step, if not, we return to the (b).
5. We make the time projection, that means that we solve the system: , where :
6. Then we go to the first step.