A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels

-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the case of non-smooth kernel, it is justified that the start-up singularities can be resolved at superconvergence rates by using non-uniformly graded meshes. Our theoretical...

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Bibliographic Details
Published in:Mathematics of computation 2013-10, Vol.82 (284), p.1987-2005
Main Author: MUSTAPHA, KASSEM
Format: Article
Language:English
Subjects:
Approximation
Error analysis
Error rates
Estimation methods
Galerkin methods
Mathematical problems
Orthogonality
Spectral methods
Textual collocation
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Summary:-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the case of non-smooth kernel, it is justified that the start-up singularities can be resolved at superconvergence rates by using non-uniformly graded meshes. Our theoretical results are numerically validated in a sample of test problems.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2013-02689-0