Fast estimation of discretization error for FE problems solved by domain decomposition

TL;DR

This paper introduces a parallelizable a posteriori error estimation method for finite element problems solved via non-overlapping domain decomposition, enabling efficient and accurate discretization error assessment during iterative solutions.

Contribution

It proposes a novel fully parallel error estimation strategy applicable to primal and dual domain decomposition methods, effective even before solver convergence.

Findings

Efficient error estimation with minimal iterations

Applicable to both BDD and FETI methods

Supports adaptive computational strategies

Abstract

This paper presents a strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in constitutive relation for linear mechanical problems. Our method allows to compute error estimate in a fully parallel way for both primal (BDD) and dual (FETI) approaches of non-overlapping domain decomposition whatever the state (converged or not) of the associated iterative solver. Results obtained on an academic problem show that the strategy we propose is efficient in the sense that correct estimation is obtained with fully parallel computations; they also indicate that the estimation of the discretization error reaches sufficient precision in very few iterations of the domain decomposition solver, which enables to consider highly effective adaptive computational strategies.