Adaptive selection of polynomial degrees on a finite element mesh

The problem of nding a nearly optimal distribution of polynomial degrees on a xed nite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector eld computed from the nite element solution. This estimator, designed for p- and hp-extensions, is conceptually di erent from estimators based on residuals or patch recovery which are designed for h-extension procedures. The quality of the error estimator is demonstrated by examples. The results show that the e ectivity index is reasonably close to unity and the sequences of p-distributions obtained with the error indicators closely follow the optimal trajectory