A priori error estimates of Adams-Bashforth discontinuous Galerkin methods for scalar nonlinear conservation laws
Charles Puelz, Beatrice Riviere
TL;DR
This paper establishes theoretical convergence and error estimates for Adams-Bashforth and forward Euler discontinuous Galerkin methods applied to scalar nonlinear conservation laws, highlighting optimal temporal rates and suboptimal spatial rates under CFL conditions.
Contribution
It provides the first a priori error estimates for Adams-Bashforth DG methods and extends convergence analysis to these time-stepping schemes for nonlinear conservation laws.
Findings
Optimal convergence rates in time for the Adams-Bashforth method
Suboptimal convergence rates in space for the DG methods
Error estimates valid under CFL conditions
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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Taxonomy
TopicsComputational Fluid Dynamics and Aerodynamics · Advanced Numerical Methods in Computational Mathematics · Fluid Dynamics and Turbulent Flows
A priori error estimates of Adams–Bashforth
discontinuous Galerkin methods for scalar nonlinear conservation laws
Charles Puelz and Béatrice Rivière