Finite element approximation of an obstacle problem for a class of integro-differential operators
arXiv:1808.0157613 citationsh-index: 26
AI Analysis
Provides theoretical regularity and numerical analysis for a class of nonlocal obstacle problems, relevant to applied mathematicians working on PDEs and numerical methods.
The authors prove regularity results for the solution of an obstacle problem involving a second-order elliptic operator and the integral fractional Laplacian, and use these to design and analyze a finite element scheme.
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.