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Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations. (English) Zbl 1348.78028
The paper under review deals with the study of the first order divergence-free method in connection with Cartesian meshes for the magnetic induction equations. This study is in strong relationship with the stability and numerical analysis of solutions of the ideal magneto-hydrodynamic equations. The authors are mainly concerned with the numerical stability, which is established through both energy and Fourier methods. This study is performed when the meshes are uniform and when the velocity field in the equations is constant. The authors also establish a priori error estimates in the $$L^2$$ norm for sufficiently smooth solutions.

##### MSC:
 78M25 Numerical methods in optics (MSC2010) 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 35L50 Initial-boundary value problems for first-order hyperbolic systems
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