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IMPLEMENTATION OF HIGH-ORDER, DISCONTINUOUS GALERKIN TIME STEPPING FOR FRACTIONAL DIFFUSION PROBLEMS

Part of: Numerical approximation and computational geometry Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  06 November 2020

WILLIAM MCLEAN Open the ORCID record for WILLIAM MCLEAN [Opens in a new window]
WILLIAM MCLEAN*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW2052, Australia; e-mail: w.mclean@unsw.edu.au.
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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.

Keywords

Gauss quadraturefinite-element methodLegendre polynomialsreconstructionsuperconvergence

MSC classification

Primary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Secondary: 65D30: Numerical integration
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 2 , April 2020 , pp. 121 - 147
Copyright
© Australian Mathematical Society 2020

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