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

TL;DR

This paper investigates the regularity of solutions to an obstacle problem involving elliptic and fractional Laplacian operators, and uses this to develop and analyze a finite element numerical scheme.

Contribution

It provides new regularity results for the obstacle problem with integro-differential operators and applies these results to finite element method design and analysis.

Findings

Established solution smoothness for the obstacle problem

Designed a finite element scheme based on regularity results

Analyzed the convergence and stability of the scheme

Abstract

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.