One of the important properties for the solutions of Maxwell equations is the conservation of the electric and magnetic charges. But, these charge conservation laws, mathematically described by elliptic divergence equations, are not strictly obeyed by numerical solutions of Maxwell and MHD equations, due to the presence of various types of numerical errors. In this paper, an extension of the recently proposed Generalized Lagrange Mutiplier (GLM) divergence correction scheme for the Maxwell- and MHD equations is investigated. The underlying idea has been verified by some simple test problems, and further generalization of the method is proposed. In particular, a possible numerical violation of the quasineutrality condition in indeal MHD is issued, and a new correction strategy is presented.

KEYWORDS: Divergence correction, Maxwell theory, Mangetohydrodynamics,

GLM method, quasineutrality