On The Long-time H~2-stability Of The Implicit Euler Scheme For The 2d Magnetohydrodynamics Equations

摘要

Pursuing our work in Tone (Asymptot. Analysis 51:231-245, 2007) and Tone and Wirosoetisno (SIAM J. Number. Analysis 44:29-40, 2006), we consider in this article the two-dimensional magnetohydrodynamics equations, we discretize these equations in time using the implicit Euler scheme and with the aid of the classical and uniform discrete Gron-wall lemma, we prove that the scheme is H~2-uniformly stable in time.