Defeaturing Error Estimates for Poisson Problems with Dirichlet Features
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Geometry simplification, also known as defeaturing, is crucial for industrial simulations. It not only simplifies the meshing process but also reduces the computational costs of subsequent simulations by decreasing the number of degrees of freedom. Traditional defeaturing methods often rely on geometric criteria alone, overlooking the underlying physics of the problem. In contrast, analysis-aware defeaturing employs a posteriori error estimation, combining the defeatured simulation outputs with the exact geometry information to better inform the defeaturing process.
A rigorous mathematical framework exists for analysis-aware defeaturing for the Poisson problem, linear elasticity, and Stokes flow. Reliable a posteriori estimators have been developed to evaluate the defeaturing error in terms of the energy norm associated with these PDE problems. However, previous works have been restricted to cases where Neumann boundary conditions are applied at the feature boundaries. Additionally, in many applications, the energy norm is not the primary quantity of interest but rather linear functionals of the solution.
Our contributions are as follows: First, we extend the current framework and provide reliable defeaturing error estimators for the Poisson problems with features subject to Dirichlet boundary conditions. Second, we derive reliable error estimates for linear functionals of the solution based on the dual weighted residual method and the energy norm estimates. Finally, we provide numerical examples in two and three dimensions that validate the validity and efficiency of the estimators.