A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods

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

1 LMT - Laboratoire de Mécanique et Technologie

This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We propose a new strict upper bound of the error which separates the contribution of the iterative solver and the contribution of the discretization. Numerical assessments show that the bound is sharp and enables us to define an objective stopping criterion for the iterative solver

Mots clés: Convergence criterion; Verification; Domain decomposition methods; FETI; BDD; Convergence criterion.

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

Valentine Rey, Christian Rey, Pierre Gosselet. A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods. Computer Methods in Applied Mechanics and Engineering, 2014, 270, pp.293-303. ⟨10.1016/j.cma.2013.12.001⟩. ⟨hal-00919435⟩