Optimal meshes and h-p adaptivity

This paper concerns the theory and implementation of the p and h-p adaptive versions of the finite element method. The different procedures of adaptivity and the optimal mesh concept are discussed and a methodology to obtain optimal or quasi optimal meshes with hierarchical elements is presented. The error estimator used and the algorithm implemented are also presented. The efficiency is demonstrated in two classical 2D examples. In this examples, we have analysed both cases the regular solution and non-regular one, and the meshes obtained during the adaptive processes are compared.