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

Authors

Keywords:

Gauss quadrature, finite-element method, Legendre polynomials, reconstruction, superconvergence

Abstract

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 specialized 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.

doi: 10.1017/S1446181120000152

Author Biography

William McLean, School of Mathematics and Statistics The University of New South Wales Sydney 2052

Associate Professor Dept of Applied Mathematics

Published

2021-01-13

Issue

Section

Articles for Printed Issues