A variational approach to optimal meshes (Q1923320)

A variational approach for optimization of triangular or tetrahedral meshes is considered. The existence and under stronger conditions the global injectivity of an optimal solution in the class of admissible variations are proved. It is possible to improve and adapt 3-dimensional meshes by a stable minimization algorithm with useful properties. The reconstruction of the grid for a domain with free boundary, the concentration of the mesh at singularities, or its compression near an arbitrary given boundary to resolve a boundary layer are interesting applications.