Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods

Abstract

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a DD iterative solver) from the discretization error (due to the FE), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal-oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions.

International Journal for Numerical Methods in Engineering, Wiley, 2016

References in corpus (5)

• On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples
• Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems
• A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods
• Study of the strong prolongation equation for the construction of statically admissible stress fields: implementation and optimization
• Strict bounding of quantities of interest in computations based on domain decomposition