A FRACTIONAL LAPLACE EQUATION: REGULARITY OF SOLUTIONS AND FINITE ELEMENT APPROXIMATIONS

J. P. BORTHAGARAY; G. ACOSTA

SIAM JOURNAL ON NUMERICAL ANALYSIS

SIAM PUBLICATIONS

Lugar: Philadelphia-USA; Año: 2017 vol. 55 p. 472 - 495

0036-1429

This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Hölder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.