Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

2010 ◽  
Vol 48 (3) ◽  
pp. 1038-1063 ◽  
Author(s):  
Qiang Zhang ◽  
Chi-Wang Shu
Keyword(s):  
Stability Analysis ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
A Priori ◽  
Scalar Conservation Laws ◽  
Third Order ◽  
The Third ◽  
Priori Error Estimates ◽  
Scalar Conservation

scholarly journals Combined DG scheme that maintains increased accuracy in areas of shock waves

2019 ◽  
Vol 489 (2) ◽  
pp. 119-124 ◽  
Author(s):  
M. E. Ladonkina ◽  
O. A. Nekliudova ◽  
V. V. Ostapenko ◽  
V.  F. Tishkin
Keyword(s):  
Shock Waves ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Nonlinear Correction ◽  
Third Order ◽  
The Third ◽  
Dg Method

A combined scheme of the discontinuous Galerkin method is proposed. This scheme monotonously localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the calculated solutions. In this scheme, a non-monotonic version of the third-order DG method is used as the baseline and a monotonic version of this method is used as the internal one, in which a nonlinear correction of numerical flows is used. Tests demonstrating the advantages of the new scheme compared to the standard monotonized variants of the DG method are provided.

Sign in / Sign up

Export Citation Format

Share Document