An optimization-based method for sign-changing ...
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Article dans une revue scientifique: Article original
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Title :
An optimization-based method for sign-changing elliptic PDEs
Author(s) :
Abdulle, Assyr [Auteur]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Lemaire, Simon [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Lemaire, Simon [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Journal title :
ESAIM: Mathematical Modelling and Numerical Analysis
Pages :
2187-2223
Publisher :
EDP Sciences
Publication date :
2024
ISSN :
0764-583X
English keyword(s) :
Sign-shifting PDEs
Metamaterials
Finite elements
Domain decomposition
Optimization
Metamaterials
Finite elements
Domain decomposition
Optimization
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition ...
Show more >We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the $\texttt{T}$-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which $\texttt{T}$-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.Show less >
Show more >We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the $\texttt{T}$-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which $\texttt{T}$-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Source :
Submission date :
2025-01-24T13:59:16Z
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