A priori error estimates of Adams-Bashforth discontinuous Galerkin methods for scalar nonlinear conservation laws
Provides rigorous error analysis for a class of numerical methods, benefiting researchers in computational PDEs, though the results are incremental as they extend existing theory to a specific time-stepping scheme.
The paper proves theoretical convergence and derives a priori error estimates for Adams-Bashforth discontinuous Galerkin methods applied to scalar nonlinear conservation laws, achieving optimal temporal and suboptimal spatial convergence rates under a CFL condition.
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.