242 citations · 611 across the 19 of their papers we have counts for
3 papers · 1 filter
Finite element approximation of fractional Neumann problems
Francisco M. Bersetche, Juan Pablo Borthagaray
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation…
Local energy estimates for the fractional Laplacian
Juan Pablo Borthagaray, Dmitriy Leykekhman, Ricardo H. Nochetto
The integral fractional Laplacian of order is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic…
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…