A Maximum Principle for Beltrami Color Flow

We study, in this work, the maximum principle for the Beltrami color flow and the stability of the flow’s numerical approximation by finite difference schemes. We discuss, in the continuous case, the theoretical properties of this system and prove the maximum principle in the strong and the weak formulations. In the discrete case, all the second order explicit schemes, that are currently used, violate, in general, the maximum principle. For these schemes we give a theoretical stability proof, accompanied by several numerical examples.