This research is a continuation of the past NSF-supported work on the theory and practice of the p-and h-p versions of the finite element method. The aim is to further develop theoretical and computational aspects of the method in conjunction with its use in the engineering and industrial computation. The collaboration with a number of engineering institutions will allow the investigator to obtain essential experience with the solution of large engineering problems, and will lead to speedy transfer of the results in the engineering and industrial practice.