Mesh Movement and Metamorphosis

Abstract.

Mesh coarsening and mesh enrichment are combined with a r-refinement scheme to produce a flexible approach for mesh adaptation of time evolving domains. The robustness of this method depends heavily upon maintaining mesh quality during each adaptation cycle. This in turn is inlfuenced by the ability to identify and remove badly shaped elements after the r-refinement stage. Measures of both element quality and element deformation can be defined in terms of unitarily invariant matrix norms. The construction of these element deformation and quality measures is described, and details are provided of the three stages of the adaptation cycle.