Variational Mesh Adaptation Methods

Abstract

In this chapter and the following one, we discuss the general mesh generation problem. The first main class of methods we consider are variational methods. They are applicable for either nonadaptive or adaptive mesh generation, and natural relationships between these two different goals are examined. While mesh generation ideas generally apply for either the static or dynamic case, we often limit discussion to static mesh generation since extending it to compute a dynamic mesh is straightforward in principle using the MMPDE approach discussed in § 6.1.2 (see also see § 2.3). Although variational methods have most commonly been used for finite difference computations for structured meshes, they can also be employed for unstructured mesh generation and adaptation (e.g., see Cao, Huang, and Russell [81]) and for mesh smoothing (e.g., see Canann et al. [79] and Knupp [215]).