A priori error estimates for interior penalty versions of the local discontinuous Galerkin method applied to transport equations

2001 ◽  
Vol 17 (6) ◽  
pp. 545-564 ◽  
Author(s):  
Clint Dawson ◽  
Jennifer Proft
Keyword(s):  
Galerkin Method ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
A Priori ◽  
Local Discontinuous Galerkin Method ◽  
A Priori Error Estimates ◽  
Interior Penalty ◽  
Local Discontinuous Galerkin ◽  
Priori Error Estimates

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

2018 ◽  
Vol 26 (3) ◽  
pp. 151-172
Author(s):  
Charles Puelz ◽  
Béatrice Rivière
Keyword(s):  
Conservation Laws ◽  
Galerkin Method ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Nonlinear Conservation Laws ◽  
Priori Error Estimates ◽  
Forward Euler

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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