Hierarchical mesh adaptation of 2D quadrilateral elements

In this paper, we present some examples which illustrate the use of adaptive finite element analysis using a new hierarchical refinement algorithm for 2D quadrilateral elements. Projection type a posteriori error estimators based on a global stress smoothing and a simple stress averaging scheme have been used. The algorithm produces well refined meshes for some simple examples which contain stress singularities and stress concentrations. The convergence of the energy norm error has been found to be improved over a previous simple splitting algorithm.