Mesh Generation and Mesh Adaptivity

In this chapter, we are concerned with mesh-generation methods and mesh-adaptivity issues. Many techniques are nowadays available to complete meshes of arbitrary domains for computational purposes. Planar, surface, and volume meshing have been automated to a large extent. Over the last few years, meshing activities have been focused on adaptive schemes, where the features of a solution field must be accurately captured. To this end, meshing techniques must be revisited in order to be capable of completing high-quality meshes conforming to these features. Error estimates are therefore used to analyze the solution field at a given stage, and, on the basis of the results of the infunction they yield, adapted meshes are created before computing the next stage of the solution field. A number of novel meshing issues must be addressed, including how to construct a mesh that can adapt to what the error estimate prescribes, how to handle large-size meshes, how to consider moving boundary problems, and so on. Keywords: mesh generation; mesh adaptation; adaptivity; h-method; adaptive computation; parallel meshing; moving boundary problems; FEM applications; CFD; solid mechanics