Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

DOI10.1051/m2an:2005051zbMath1084.76046OpenAlexW2116093909MaRDI QIDQ5715741

Nicolas Besse, Dietmar B. Kröner

Publication date: 5 January 2006

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2005__39_6_1177_0

zbMATH Keywords

CFL conditionsecond-order Runge Kutta time discretization

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items

A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System, On stability of numerical schemes via frozen coefficients and the magnetic induction equations, Higher order finite difference schemes for the magnetic induction equations, A priori error analysis of a discontinuous Galerkin scheme for the magnetic induction equation, Optimal error estimates of an IPDG scheme for the resistive magnetic induction equation, Stabilized discontinuous Galerkin scheme for the magnetic induction equation, Magnetic charges or why it is sometimes reasonable to model something mathematically that does not exist at all, Roe-type schemes for shallow water magnetohydrodynamics with hyperbolic divergence cleaning, Finite-volume schemes for Friedrichs systems with involutions, Interior penalty discontinuous Galerkin method for magnetic induction equation with resistivity, A global divergence conforming DG method for hyperbolic conservation laws with divergence constraint, Splitting based finite volume schemes for ideal MHD equations, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, Stable upwind schemes for the magnetic induction equation, A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

Uses Software

• ZEUS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Locally divergence-free discontinuous Galerkin methods for MHD equations
• Mixed finite elements in \(\mathbb{R}^3\)
• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
• Locally divergence-free discontinuous Galerkin methods for the Maxwell equations.
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• Hyperbolic divergence cleaning for the MHD equations
• A second order explicit finite element scheme to multi-dimensional conservation laws and its convergence
• On a class of interpolation spaces
• Symmetric positive linear differential equations
• A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
• Finite Element Methods for Navier-Stokes Equations
• Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien
• A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• Piecewise Solenoidal Vector Fields and the Stokes Problem