Arbitrary high-order discontinuous Galerkin schemes for the magnetohydrodynamic equations

DOI10.1007/s10915-006-9101-0zbMath1176.76075OpenAlexW2006118548MaRDI QIDQ879998

Arne Taube, Claus-Dieter Munz, Michael Dumbser, Dinshaw S. Balsara

Publication date: 10 May 2007

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-006-9101-0

zbMATH Keywords

magnetohydrodynamicsgeneralized Riemann problemdiscontinuous Galerkin finite elementsADER approachCauchy-Kovalevskaya procedureflux expansion

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05)

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Cites Work

• Unnamed Item
• Unnamed Item
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
• Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
• ADER: Arbitrary high-order Godunov approach
• ADER schemes for three-dimensional non-linear hyperbolic systems
• A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes
• Arbitrary high order discontinuous Galerkin schemes
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Solution of the generalized Riemann problem for advection–reaction equations
• Notes on the Eigensystem of Magnetohydrodynamics
• Divergence-free adaptive mesh refinement for magnetohydrodynamics.