| Issue |
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
|
|
|---|---|---|
| Page(s) | 229 - 253 | |
| DOI | https://doi.org/10.1051/m2an/2019058 | |
| Published online | 27 January 2020 | |
Finite element approximation of an obstacle problem for a class of integro–differential operators
1
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: bonito@math.tamu.edu
Received:
4
August
2018
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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