Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation
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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.
KeywordsNon-uniform time steps Memory term Finite elements
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