Some numerical experiences on reliability and robustness of high degree finite elements

Reliability of finite element solutions has become an important issue in the framework of the general process of solution of engineering problems via finite element techniques. In the standard procedure a finite element solution is achieved by refining the mesh parameter while using low order elements, generally of degree one or two (h version). In the last years a new version has been proposed: the solution is seeked for by increasing the degree of approximation while keeping fixed the decomposition (p version). The combination of the two versions, namely the h-p version, has proved to be a quite effective procedure. In this note we address the problem of the reliability of solutions obtained with high order finite elements. We have solved several problems with high degree elements. We show how reliability is dramatically improved by using hierarchic families of high order finite elements.