Finite elements for problems involving the fractional laplace operator

G. ACOSTA

Santa Fé, New Mexico

Workshop; MANNA 2017; 2017

SANDIA LABS and Brown University

In this talk we review some recent developments [1,2,3,4] concerning FE approximations for fractional equations involving the operator $(-\Delta)^s$. The talk is mainly devoted to steady-stateproblems although some extensions to evolution equations are also discussed.References:[1] G. Acosta, J.P. Borthagaray and N. Heuer, Finite element approximations of the nonhomogeneous fractional Dirichlet problem, Preprint ArXiv 2017.[2] G. Acosta, F. M. Bersetche and J. P. Borthagaray, A shorth FE implementation for a 2d homogeneous Dirichlet problem of a Fractional Laplacian. Comput. Math. Appl. (74) No.4, pp. 784-816, (2017).[3] G. Acosta, J. P. Borthagaray, O. Bruno and M. Maas, Regularity theory and high order numerical methods for the (1D)-Fractional Laplacian. to appear in Math. Comp.[4] G. Acosta and J. P. Borthagaray, A fractional Laplace equation: regularity of solutions and Finite Element approximations SIAM J. Numer. Anal. (55) No. 2, pp. 472-495 (2017).