Numerical comparison of some Hessian recovery techniques

Derivative recovery techniques are used in a posteriori error indicators to drive mesh adaptation. Their behaviour in the core of the computational domain and on boundaries constitutes an important efficiency factor for a subsequent mesh adaptation process. A methodology to compare recovery techniques for second-order derivatives from a piecewise linear approximation is presented in this paper. A systematic approach to measuring the performance of recovery techniques using analytical functions interpolated on a series of meshes is proposed. The asymptotic behaviour of some recently published recovery techniques, as well as new ones, is numerically assessed on various type of meshes. Recommendations are done on the choice of a recovery technique. Copyright q 2007 John Wiley & Sons, Ltd.