Application of a combined continuous–discontinuous Galerkin finite element method for the solution of the Girkmann problem

In January 2008, the International Association of Computational Mechanics (IACM) invited the scientific community to solve the Girkmann problem by finite element methods. The challenge was to get certain quantities of interest in terms of the approximate solutions within 5% of accuracy of their exact counterparts. For instance, the goal could be to evaluate the bending moment or the shear force at the junction of the shell and the ring. The purpose of the present paper is to solve an axisymmetric solid elastic model for this problem using a continuous finite element method in combination with discontinuous interface elements in the region of interest (named as the DG-FEM method). The numerical results of the pp version of the DG-FEM method are presented and discussed. The results are verified with respect to previous results published in the literature showing excellent consistent results.