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arXiv · 1301.6778

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

Kassem Mustapha
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Abstract

We study the numerical solution for Volerra integro-differential equations with smooth and non-smooth kernels. We use a $h$-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.

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Kassem Mustapha. 2013-01-28. A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels. https://arxiv.org/abs/1301.6778

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