A fews snags in mesh adaptation loops

Abstract

The first stage in an adaptive finite element scheme (cf. [CAS95, bor1]) consists in creating an initial mesh of a given domain Ω, which is used to perform an initial computation (for example a flow solver). A size specification field is deduced (e.g. at the vicinity of each mesh vertex, the desired mesh size is specified), based on the numerical results. If the mesh does not satisfy the size specification field, then a new constrained mesh, governed by this field, is constructed. The size specification field is usually obtained via an error estimate [FOR, VER96]. Actually, the estimation gives a discrete size specification field. Using an adequate size interpolation over the mesh elements, a continuous field is then obtained. © 2005 Springer-Verlag Berlin Heidelberg.