Strict upper and lower bounds for quantities of interest in static response sensitivity analysis

TL;DR

This paper introduces a goal-oriented error estimation method using CRE for finite element analysis, providing strict bounds on quantities of interest related to static response sensitivity derivatives, validated through numerical experiments.

Contribution

It presents a novel technique for obtaining strict upper and lower bounds of QoIs in static response sensitivity analysis using CRE-based error estimation.

Findings

The method effectively bounds quantities of interest in FEA.

Numerical results confirm the strict bounding properties.

The approach enhances reliability in sensitivity analysis.

Abstract

In this paper, a goal-oriented error estimation technique for static response sensitivity analysis is proposed based on the constitutive relation error (CRE) estimation for finite element analysis (FEA). Strict upper and lower bounds of various quantities of interest (QoI) that are associated with the response sensitivity derivative fields are acquired. Numerical results are presented to assess the strict bounding properties of the proposed technique.