Strict bounding of quantities of interest in computations based on domain decomposition

Bornes strictes sur des quantités d'intérêt calculées par décomposition de domaine

Valentine Rey (1) , Pierre Gosselet (1) , Christian Rey (1)

1 LMT - Laboratoire de Mécanique et Technologie

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.

Mots clés: local refinement; quantity of interest; non-overlapping domain decomposition methods; Verification

Domaines: Mécanique des structures [physics.class-ph]

Valentine Rey, Pierre Gosselet, Christian Rey. Strict bounding of quantities of interest in computations based on domain decomposition. Computer Methods in Applied Mechanics and Engineering, 2015, 287, pp.212-228. ⟨10.1016/j.cma.2015.01.009⟩. ⟨hal-01113852⟩