Adaptive refinement in defeaturing problems via an equilibrated flux a posteriori error estimator

Abstract

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and reduce the computational cost of simulations. It is a common procedure, for example, in computer aided design for simulation-based manufacturing. However, depending on the problem at hand, geometrical simplification may significantly deteriorate the accuracy of the solution. The proposed adaptive strategy is hence twofold: starting from a defeatured geometry, it performs both standard mesh refinement and geometrical refinement by selecting, at each step, which features must be reintroduced to significantly improve accuracy. Similar adaptive strategies have been previously developed using residual-based error estimators within an IGA framework. Here, instead, we extend a previously developed equilibrated flux a posteriori error analysis, designed for standard finite element discretizations, to make it fully applicable within the adaptive procedure. In particular, we address the assembly of the equilibrated flux estimator in presence of elements trimmed by the boundary of included features, adopting a CutFEM strategy to handle feature inclusion. The resulting estimator allows us to bound both the defeaturing and the numerical sources of error, with additional contributions accounting for the weak imposition of boundary conditions.