Post-processing discontinuous Galerkin solutions to Volterra integro-differential equations: Analysis and simulations

• Autores: Kassem Mustapha, Jennifer K. Ryan
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 253, Nº 1, 2013, págs. 89-103
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.03.047
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• Resumen

  • This paper presents a superconvergence extraction technique for Volterra integrodifferential equations with smooth and non-smooth kernels. Specifically, extracting superconvergence is done via a post-processed discontinuous Galerkin (DG) method obtained from interpolating the DG solution using Lagrange polynomials at the nodal points. A global superconvergence error bound (in the L��-norm) is established. For a nonsmooth kernel, a family of non-uniform time meshes is used to compensate for the singular behaviour of the exact solution near t = 0. The derived theoretical results are numerically validated in a sample of test problems, demonstrating higher-than-expected convergence rates.