In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...

As observed by Yamazaki, the third component $b_3$ of the magnetic field can be estimated by the corresponding component $u_3$ of the velocity field in $L^{\lambda }$