A constrained transport divergence-free finite element method for Incompressible MHD equations

08/21/2020 ∙ by Lingxiao Li, et al. ∙ 0

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method,we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 16

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.