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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2024

An optimization-based method for sign-changing elliptic PDEs

Abstract

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.
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Dates and versions

hal-04140542 , version 1 (25-06-2023)
hal-04140542 , version 2 (04-02-2024)

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Assyr Abdulle, Simon Lemaire. An optimization-based method for sign-changing elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis, inPress, ⟨10.1051/m2an/2024013⟩. ⟨hal-04140542v2⟩
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