RT Journal Article
T1 An Equilibrated Flux A Posteriori Error Estimator for Defeaturing Problems
A1 Buffa, Annalisa
A1 Chanon, Ondine Chanon
A1 Grappein, Denise
A1 Vázquez Hernández, Rafael
A1 Vohralik, Martin
K1 Geometric defeaturing problems
K1 A posteriori error estimation
K1 Equilibrated flux
AB An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are considered not relevant for the approximation of the solution of a given PDE. In this work, the focus is on a Poisson equation with Neumann boundary conditions on the feature boundary. The estimator accounts both for the so-called defeaturing error and for the numerical error committed by approximating the solution on the defeatured domain. Unlike other estimators that were previously proposed for defeaturing problems, the use of the equilibrated flux reconstruction allows us to obtain a sharp bound for the numerical component of the error. Furthermore, it does not require the evaluation of the normal trace of the numerical flux on the feature boundary: this makes the estimator well suited for finite element discretizations, in which the normal trace of the numerical flux is typically discontinuous across elements. The reliability of the estimator is proven and verified on several numerical examples. Its capability to identify the most relevant features is also shown, in anticipation of a future application to an adaptive strategy.
PB Society for Industrial and Applied Mathematics
SN 0036-1429
YR 2024
FD 2024
LK https://hdl.handle.net/10347/40971
UL https://hdl.handle.net/10347/40971
LA eng
NO Buffa, A., Chanon, O., Grappein, D., Vázquez, R., & Vohralik, M. (2024). AN EQUILIBRATED FLUX A POSTERIORI ERROR ESTIMATOR FOR DEFEATURING PROBLEMS. SIAM Journal on Numerical Analysis, 62(6), 2439-2458. https://doi.org/10.1137/23M1627195
NO The authors acknowledge the support of the Swiss National Science Foundation (via project MINT n. 200021 215099, PDE tools for analysis-aware geometry processing in simulation science) and of European Union Horizon 2020 FET program (under grant agreement 862025 (ADAM2)). The second author acknowledges the support of the Swiss National Science Foundation through the project n.P500PT 210974. \\dagger MNS, Institute of Mathematics, Ecole\\' Polytechnique F\\e'd\\e'rale de Lausanne, Switzerland, and IMATI CNR, 27100 Pavia, Italy (annalisa.buffa@epfl.ch). \\ddagger ABB Corporate Research Center, Baden-D\\a\"ttwil, Switzerland (ondine.chanon@ch.abb.com). \\S Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino, Italy, Member of GNCS INdAM Group (denise.grappein@polito.it). Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Spain (rafael.vazquez@usc.es). \\| Inria, 75589 Paris, France, and CERMICS, Ecole des Ponts, 77455 Marne-la-Valle'e, France (martin.vohralik@inria.fr).
DS Minerva
RD 24 abr 2026