ANISOTROPIC MESH TRANSFORMATIONS AND OPTIMAL ERROR CONTROL

Recently, research originating in several different applications has appeared on unstructured triangular meshes in which the vertex distribution is not locally uniform, i.e. anisotropic unstructured meshes. The techniques used have the common features that the distribution of triangle shapes for the mesh is controlled by specifying a symmetric tensor, and that the anisotropic mesh is the transform of an isotropic mesh. We discuss how these mechanisms arise in the theory of optimal error control, using simple model mesh generation problems, and review the related research in applications to computational fluid dynamics, surface triangulation, and semiconductor simulation.