no. 1
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

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
Keywords: 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},
     year = {2020},
     publisher = {EDP Sciences},
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     mrnumber = {4055457},
     language = {en},
     url = {https://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

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