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Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains
Juan Pablo Borthagaray, Ricardo H. Nochetto
We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order in bounded Lipschitz domains : \[ \begin{a…
Constructive approximation on graded meshes for the integral fractional Laplacian
Juan Pablo Borthagaray, Ricardo H. Nochetto
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian . We prove optimal Sobolev regularity estimates in Lipschitz domains provided the soluti…
Numerical analysis of the LDG method for large deformations of prestrained plates
Andrea Bonito, Diane Guignard, Ricardo Nochetto +1
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our prev…
Finite element algorithms for nonlocal minimal graphs
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a…
Gamma-convergent projection-free finite element methods for nematic liquid crystals: The Ericksen model
Ricardo H. Nochetto, Michele Ruggeri, Shuo Yang
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable, and allows the formation of various defects with finite energy…
Robust BPX Preconditioner for Fractional Laplacians on Bounded Lipschitz Domains
Juan Pablo Borthagaray, Ricardo H. Nochetto, Shuonan Wu +1
We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. For either quasi-uniform grids or graded bisection grids, we…