Finite element approximation of an obstacle problem for a class of integro–differential operators

Bonito, Andrea; Lei, Wenyu; Salgado, Abner J.

doi:10.1051/m2an/2019058

Bonito, Andrea ; Lei, Wenyu ; Salgado, Abner J.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 229-253.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

We study the regularity of the solution to an obstacle problem for a class of integro–differential operators. The differential part is a second order elliptic operator, whereas the nonlocal part is given by the integral fractional Laplacian. The obtained smoothness is then used to design and analyze a finite element scheme.

DOI : 10.1051/m2an/2019058

Classification : 35R11, 35R35, 41A29, 65K15, 65N15, 65N30
Mots-clés : Obstacle problem, free boundaries, integro–differential operators, finite elements, Dunford–Taylor integral

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     title = {Finite element approximation of an obstacle problem for a class of integro{\textendash}differential operators},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {229--253},
     publisher = {EDP-Sciences},
     volume = {54},
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     year = {2020},
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     mrnumber = {4055457},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2019058/}
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Bonito, Andrea; Lei, Wenyu; Salgado, Abner J. Finite element approximation of an obstacle problem for a class of integro–differential operators. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 229-253. doi : 10.1051/m2an/2019058. http://www.numdam.org/articles/10.1051/m2an/2019058/

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