A goal-oriented error estimator for the analysis of simplified designs

Simplifying an engineering design by removing geometric details can significantly reduce the complexity of downstream tasks of mesh generation and field solution computation. However, lack of a proper analysis and estimates of the errors induced by design simplification remains a bottleneck in seamless CAD/CAE integration. To address this issue, this paper develops a general framework for providing a posteriori estimates of goal-oriented engineering analysis error caused by removing a negative feature, or void, where material is absent, from an engineering design. Our approach is built upon the idea of representing it as a modeling error defined in the same geometry, which is then estimated using the dual weighted residual method. The derived error estimator still involves an uncomputable term involving dual errors, which is removed by further simplification into a term on the feature's boundary, via an exterior solution in linear cases or problem-specific approaches in nonlinear cases, utilizing classical theories of differential operators. We illustrate our approach via a semilinear second order elliptic equation, and explicit error estimators are also derived for the classical Poisson equation and linear elasticity. Results of numerical tests are shown, and comparisons made with results obtained with related approaches.