Volume 54, Number 1, January-February 2020
|Page(s)||229 - 253|
|Published online||27 January 2020|
Finite element approximation of an obstacle problem for a class of integro–differential operators
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
2 SISSA – International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
3 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
* Corresponding author: firstname.lastname@example.org
Accepted: 1 August 2019
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.
Mathematics Subject Classification: 35R11 / 35R35 / 41A29 / 65K15 / 65N15 / 65N30
Key words: Obstacle problem / free boundaries / integro–differential operators / finite elements / Dunford–Taylor integral
© EDP Sciences, SMAI 2020
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