Adaptive selection of polynomial degrees on a finite element mesh

Abstract

The problem of ÿnding a nearly optimal distribution of polynomial degrees on a ÿxed ÿnite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector ÿeld computed from the ÿnite 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. ? 1998 John Wiley & Sons, Ltd.KEY WORDS: ÿnite element method; adaptivity; a posteriori error estimation

HAMILTONIAN AS ERROR INDICATOR IN THE P-VERSION OF FINITE ELEMENT METHOD

“…3. For adaptive p-version (see Table 1), the optimal values of p are 2, 5, 8 and 5 for elements 1 through 4, respectively, which are consistent with Ref [18]. Thus, Error(Res) is suitable for the adaptive p-version.…”

“…A square panel under parabolic edge load shown in Fig. 5(a) is studied [18]. Three meshes are investigated as follows, and error analysis is compared to each other.…”

An adaptive strategy for hp-FEM based on testing for analyticity

“…The approach pursued in [11,12] consists in formulating hp-adaptivity as an optimization problem of finding the most efficient combination of h-refinement and p-enrichment. Earlier work consists of the Texas Three Step of [9,28,29].…”