Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical sol...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2009-09, Vol.231 (2), p.735-744
Main Author: Mustapha, Kassem
Format: Article
Language:English
Subjects:
Acceleration of convergence
Calculus of variations and optimal control
Discontinuous Galerkin method
Error estimates
Exact sciences and technology
Finite element method
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Smooth kernel
Sub-diffusion
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Summary:In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.04.020