1 citations · 1 across the 3 of their papers we have counts for
8 papers
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…
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…
The -tensor Model with Uniaxial Constraint
Juan Pablo Borthagaray, Shawn W. Walker
This chapter is about the modeling of nematic liquid crystals (LCs) and their numerical simulation. We begin with an overview of the basic physics of LCs and discuss some of their…
A structure-preserving FEM for the uniaxially constrained -tensor model of nematic liquid crystals
Juan Pablo Borthagaray, Ricardo H. Nochetto, Shawn W. Walker
We consider the one-constant Landau - de Gennes model for nematic liquid crystals. The order parameter is a traceless tensor field , which is constrained to be uniaxial…
Linear and Nonlinear Fractional Elliptic Problems
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. T…
Finite element discretizations of nonlocal minimal graphs: convergence
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
In this paper, we propose and analyze a finite element discretization for the computation of fractional minimal graphs of order~ on a bounded domain . Such a Plat…