Finite element approximation of fractional Neumann problems

08/13/2020
by   Francisco M. Bersetche, et al.
0

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 of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method's performance as well as certain properties of solutions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/10/2019

Linear and Nonlinear Fractional Diffusion

This paper surveys recent analytical and numerical research on linear pr...
research
05/13/2021

Finite element algorithms for nonlocal minimal graphs

We discuss computational and qualitative aspects of the fractional Plate...
research
01/28/2021

A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applicat...
research
06/17/2019

A parallel-in-time multigrid solver with a new two-level convergence for two-dimensional unsteady fractional Laplacian problems

The multigrid-reduction-in-time (MGRIT) technique has proven to be succe...
research
12/17/2019

On the finite element approximation for fractional fast diffusion equations

Considering fractional fast diffusion equations on bounded open polyhedr...
research
01/13/2021

Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

We consider numerical approximation of spectral fractional Laplace-Beltr...

Please sign up or login with your details

Forgot password? Click here to reset