Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 39, Issue 3, Pages 1471-1501Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/dry023
Keywords
fractional Laplacian; mixed finite elements; a priori error analysis
Categories
Funding
- Comision Nacional de Investigacion Cientifica y Tecnologica-Chile Fondecyt project [1150056]
- National Scientific and Technical Research Council [PIP 2014-2016 11220130100184CO]
- Agencia Nacional de Promocion Cientifica y Tecnologica [2014-1771]
Ask authors/readers for more resources
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogue of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed both for the solution and for its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available