Efficiency of refinement procedures for the p‐version of the adaptive finite element method

Presents an efficiency study of different refinement procedures for the p‐version of the adaptive finite element method in two‐dimensional elasticity problems. The refinement strategy, based on the estimated error in energy norm, attempts an optimal distribution of the nodeless degrees of freedom associated with the basic approximation parameter of the order p of the hierarchical shape functions. This procedure is combined with appropriate matrix‐handling techniques and equation solvers in order to achieve a solution of a given accuracy with the minimum computational resources in terms of computing time and storage. To this extent, convergence studies are performed with constant and variable adaptivity indices, with error estimators based on global and elemental approaches and with domain decomposition matrix‐handling techniques and the preconditioned conjugate gradient solver.