Robust possibilities for mesh-motion are crucial for solving problems in fluid-structure interaction using the Arbitrary Lagrangian Eulerian (ALE) approach as well as in structural optimization.
Thus in fluid-structure interaction the mesh has to be able to reproduce the motion of the structure in the fluid domain and in structural optimization the mesh has to move according to the changes of the structure due to the optimization algorithm. If updating the mesh is not working in a reliable manner, the simulation will produce inexact results or will even fail completely.
The possibility of re-meshing is mostly computational expensive and might lead to loss of information, when mapping the information from the old to the new mesh. Hence for fluid-structure interaction problems, in case they are treated by the Arbitrary Lagrangian Eulerian approach, a robust and efficient mesh-updating technique is necessary.