DeepAI AI Chat
Log In Sign Up

Analysis of a sinc-Galerkin Method for the Fractional Laplacian

by   Harbir Antil, et al.
George Mason University

We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-function based method to solve fractional PDEs. While the original method was formulated as a collocation method, we show that the same method can be interpreted as a nonconforming Galerkin method, giving access to abstract error estimates. Optimal order of convergence is shown without any unrealistic regularity assumptions on the solution.


page 1

page 2

page 3

page 4


Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian

In this paper, we provide a framework of designing the local discontinuo...

On spectral Petrov-Galerkin method for solving fractional initial value problems in weighted Sobolev space

In this paper, we investigate a spectral Petrov-Galerkin method for frac...

Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations

Two numerical methods with graded temporal grids are analyzed for fracti...

A unified meshfree pseudospectral method for solving both classical and fractional PDEs

In this paper, we propose a meshfree method based on the Gaussian radial...

A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen–Loève expansion

Numerical computation of the Karhunen–Loève expansion is computationally...