Numeerisen analyysin ja laskennallisen tieteen seminaari

26.9.2005 klo 14.15 U356

Marcus Rüter, Sergey Korotov, and Christian Steenbock,
TKK Matematiikan laitos

A Posteriori Error Estimates in Linear Elastic Fracture Mechanics based on Different FE-Solution Spaces for the Primal and the Dual Problem

The objective of this presentation is to derive goal-oriented a posteriori error estimators for the error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the finite element method. Such error estimators are based on the well- established strategy of solving an auxiliary dual problem. In a straightforward fashion, the solution to the dual problem is sought in the same FE-space as the solution to the primal problem, i.e. on the same mesh, although it merely acts as a weight of the discretization error only. In this paper, we follow the strategy recently proposed by Korotov et al. and derive goal-oriented error estimators of the averaging type, where the dual solution is computed on a different, usually coarser, mesh than the primal solution. On doing so, the FE-solution to the primal problem has to be transferred into the FE-solution space of the dual problem. The necessary algorithms, which are implemented in Matlab, are briefly explained and finally some illustrative numerical examples are presented.