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.