Strict bounding of quantities of interest in computations based on domain decomposition
arXiv:1502.02887 · doi:10.1016/j.cma.2015.01.009
Abstract
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems : on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver. Beside practical considerations on the parallel computation of the bounds, it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation. Academic assessments are given on 2D static linear mechanic problems.
arXiv commentComputer Methods in Applied Mechanics and Engineering, Elsevier, 2015, online preview
References in corpus (5)
- Non-overlapping domain decomposition methods in structural mechanics
- On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples
- A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods
- Fast estimation of discretization error for FE problems solved by domain decomposition
- Study of the strong prolongation equation for the construction of statically admissible stress fields: implementation and optimization