An explicit discontinuous Galerkin scheme based on a Runge-Kutta predictor with application to magnetohydrodynamics

2012 ◽  
pp. 319-328
Author(s):  
Christoph Altmann ◽  
Gregor Gassner ◽  
Claus-Dieter Munz
Keyword(s):  
Discontinuous Galerkin ◽  
Galerkin Scheme ◽  
Discontinuous Galerkin Scheme ◽  
Runge Kutta

A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation

2020 ◽  
Vol 20 (1) ◽  
pp. 121-140 ◽  
Author(s):  
Tanmay Sarkar
Keyword(s):  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Magnetic Induction ◽  
Time Discretization ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Galerkin Scheme ◽  
Optimal Convergence ◽  
Discontinuous Galerkin Scheme ◽  
Runge Kutta

AbstractWe perform the error analysis of a stabilized discontinuous Galerkin scheme for the initial boundary value problem associated with the magnetic induction equations using standard discontinuous Lagrange basis functions. In order to obtain the quasi-optimal convergence incorporating second-order Runge–Kutta schemes for time discretization, we need a strengthened {4/3}-CFL condition ({\Delta t\sim h^{4/3}}). To overcome this unusual restriction on the CFL condition, we consider the explicit third-order Runge–Kutta scheme for time discretization. We demonstrate the error estimates in {L^{2}}-sense and obtain quasi-optimal convergence for smooth solution in space and time for piecewise polynomials with any degree {l\geq 1} under the standard CFL condition.

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