Verification of XFEM models through strict error bounds
Today, more than ever, modeling and simulation are central to any mechanical engineering activity. One of the key issues is the assessment of the quality of calculated outputs of interest obtained, for example, through finite element analysis. The objective goes beyond that of earlier error estimators, which provided only global information. Since most error estimators available today are nonconservative, the derivation of effective and guaranteed upper error bounds of calculated outputs of interest is still a challenge. The central question discussed in this paper is how one can obtain practical, effective, and guaranteed error bounds in the context of the eXtended Finite Element Method (XFEM). It is shown that the constitutive relation error method, with very few technical modifications, still works. The main idea of the CRE method is to rewrite the outputs of interest globally in order to be able to reuse global CRE estimators, such as dissipation-error-based estimators. After having introduced the adjoint problem, which depends on the quantity of interest, one can obtain guaranteed sharp bounds by solving this problem properly using local refinements in both space and time 1,2. In this presentation, we focus on technical aspects of the method which are specific to the XFEM, especially the recovery of admissible fields which is the cornerstone of the CRE estimator 3. Recent advances which simplify the coding task are also discussed 4. Finally, the technical aspects and the efficiency of the CRE method are illustrated through numerical examples related mainly to fracture mechanics.
P. Ladeveze L. Chamoin
LMT-Cachan (ENS Cachan/CNRS/UPMC/PRES UniverSud Paris), 61, avenue du President Wilson, 94235 CACHAN LMT-Cachan (ENS Cachan/CNRS/UPMC/PRES UniverSud Paris), 61, avenue du President Wilson, 94235 CACHAN
国际会议
南京
英文
4
2009-10-12（万方平台首次上网日期，不代表论文的发表时间）