Hp-Adaptive methods have been available for more than one decade [6]. Thus far, the choice of h, p or hp-refinement has been based on the a-priori knowledge of the regularity of the solution and their corresponding optimal sequence of refinement pattern [4].

The proposed strategy is implemented within the object oriented environment PZ for the development of scientific software. The following capabilities of the PZ environment were either used or added:

• Transfer of solution between meshes. A method for computing a transfer matrix between meshes is implemented based on the projection of the interpolation space of the coarse mesh onto the fine mesh;
• Development of a block diagonal preconditioner for the acceleration Krylov iterative methods; * Development of a solution class which implements the multigrid iteration process;
• A class which implements a one dimensional optimal hp refinement analysis based on the comparaison of all possible refinement patterns.

These interfaces are used to implement and edge-based adaptive hp-refinement strategy. The results show that the adaptive strategy is able to produce hp refined meshes with exponential convergence rates, even for singular problems.

Several examples show the generality and aplicability of the strategy for different simulations.