Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data

2013 ◽  
Vol 126 (4) ◽  
pp. 703-740 ◽  
Author(s):  
Qiang Zhang ◽  
Chi-Wang Shu
Keyword(s):  
Initial Data ◽  
Galerkin Method ◽  
Hyperbolic Equation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
One Dimension ◽  
Third Order ◽  
Linear Hyperbolic Equation ◽  
The Third ◽  
Discontinuous Initial Data

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.

scholarly journals A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

2011 ◽  
Vol 9 (2) ◽  
pp. 240-268 ◽  
Author(s):  
John Loverich ◽  
Ammar Hakim ◽  
Uri Shumlak
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Solutions ◽  
Three Dimensions ◽  
Third Order ◽  
Small Gauge ◽  
Electron Acoustic ◽  
Two Fluid ◽  
Two Fluid Plasma

AbstractA discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock [1] and existing numerical solutions to the GEM challenge magnetic reconnection problem [2]. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.

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