Adaptivity and mesh generation

Abstract The objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success. Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes ; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement . With h and h ‐ p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density. The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.