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

Charles Puelz 1  and Béatrice Rivière 1
  • 1 Rice University, Department of Computational and Applied Mathematics, 6100 Main MS-134, Houston, USA
Charles Puelz
  • Corresponding author
  • Rice University, Department of Computational and Applied Mathematics, 6100 Main MS-134, Houston, Texas, 77005, USA
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and Béatrice Rivière
  • Rice University, Department of Computational and Applied Mathematics, 6100 Main MS-134, Houston, Texas, 77005, USA
  • Search for other articles:
  • degruyter.comGoogle Scholar

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.

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