Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique

The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field r∗ from the finite element solution rfe. Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR-C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch r∗ p that locally satisfy the equations that should be satisfied by the exact solution. As a result the evaluated expressions for r∗ p will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field r∗ and therefore the local effectivity of the ZZ error estimator. Copyright q 2006 John Wiley & Sons, Ltd