DeepAI AI Chat
Log In Sign Up

Implementation of high-order, discontinuous Galerkin time stepping for fractional diffusion problems

by   William McLean, et al.

The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialised quadrature techniques that efficiently maintain the overall accuracy of the dG method. In addition, we observe in numerical experiments that known superconvergence properties of dG time stepping for classical diffusion problems carry over in a modified form to the fractional-order setting.


page 1

page 2

page 3

page 4


A GPU implementation of the Discontinuous Galerkin method for simulation of diffusion in brain tissue

In this work we develop a methodology to approximate the covariance matr...

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...

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...

Discontinuous Galerkin methods for magnetic advection-diffusion problems

We devise and analyze a class of the primal discontinuous Galerkin metho...

Code Repositories


Generate coefficient arrays needed for discontinuous Galerkin time-stepping of fractional diffusion problems.

view repo