Abstract
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.
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We thank the University of New South Wales for financial support provided by a Faculty Research Grant.
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McLean, W., Mustapha, K. Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer Algor 52, 69–88 (2009). https://doi.org/10.1007/s11075-008-9258-8
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DOI: https://doi.org/10.1007/s11075-008-9258-8