Adaptive modification of time evolving meshes

The accuracy of a finite element computation depends on the mesh size and the distribution of mesh points. Adapting the mesh to capture the salient features in the finite element computation can provide a much more accurate solution without imposing an excessive increase in mesh size and computational cost. When the shape of the meshed domain is evolving in time mesh adaptation is essential in order to maintain conformity of the mesh with the domain boundaries. Mesh adaptation for time evolving domains can be accomplished through a combination of mesh movement with mesh modification by selective coarsening and enrichment of various regions in the mesh. Large deformations of the computational domain and boundary can be accommodated if overall mesh quality is maintained after each adaptation cycle.