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

Kassem Mustapha

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

Numerical Analysis 2014-12-08 v1

Authors: Kassem Mustapha

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.

Keywords

Volterra integro-differential equations discontinuous Galerkin method superconvergence non-smooth kernels graded meshes error bounds

Cite

@article{arxiv.1301.6778,
  title  = {A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels},
  author = {Kassem Mustapha},
  journal= {arXiv preprint arXiv:1301.6778},
  year   = {2014}
}

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