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A priori error estimates of Adams-Bashforth discontinuous Galerkin Methods for scalar nonlinear conservation laws

Charles Puelz and Béatrice Rivière

Abstract

In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition.

MSC 2010: 65M12; 65M15; 65M60

  1. Funding: The authors are funded in part by the grants NSF-DMS 1312391 and NSF 1318348 and by a training fellowship from the Keck Center of the Gulf Coast Consortia, on the Training Program in Biomedical Informatics, National Library of Medicine (NLM) T15LM007093.

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Received: 2017-01-27
Revised: 2017-04-26
Accepted: 2017-05-08
Published Online: 2017-05-19
Published in Print: 2018-09-25

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