Numerical Algorithms

, Volume 52, Issue 1, pp 69–88 | Cite as

Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation

  • William McLean
  • Kassem Mustapha
Original Paper


We employ a piecewise-constant, discontinuous Galerkin method for the time discretization of a sub-diffusion equation. Denoting the maximum time step by k, we prove an a priori error bound of order k under realistic assumptions on the regularity of the solution. We also show that a spatial discretization using continuous, piecewise-linear finite elements leads to an additional error term of order h 2 max (1,logk  − 1). Some simple numerical examples illustrate this convergence behaviour in practice.


Non-uniform time steps Memory term Finite elements 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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