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A stabilized finite element method for a fictitious domain problem allowing small inclusions
Author(s) -
Barrenechea Gabriel R.,
González Cheherazada
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22190
Subject(s) - mathematics , finite element method , convergence (economics) , domain (mathematical analysis) , differential inclusion , partial differential equation , stability (learning theory) , mathematical analysis , work (physics) , extended finite element method , simple (philosophy) , elliptic curve , computer science , structural engineering , mechanical engineering , machine learning , engineering , economics , economic growth , philosophy , epistemology
The purpose of this work is to approximate numerically an elliptic partial differential equation posed on domains with small perforations (or inclusions). The approach is based on the fictitious domain method, and as the method's interest lies in the case in which the geometrical features are not resolved by the mesh, we propose a stabilized finite element method. The stabilization term is a simple, non‐consistent penalization that can be linked to the Barbosa‐Hughes approach. Stability and convergence are proved, and numerical results confirm the theory.