Mesh Generation and Mesh Adaptivity: Theory and Techniques

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 the information 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 adapted to what the error estimate prescribes, how to handle large size meshes, how to consider moving boundary problems, etc. Keywords: mesh generation; mesh adaptation; adaptivity; h-method; adaptive computation; parallel meshing; moving boundary problems; FEM applications; CFD; solid mechanics

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