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To preserve the divergence constraints on the electric and magnetic fields two different approaches are used.
By analogy with the idea developed, we propose a method based on the dualization and then the approximation of the interface conditions in a way consistent with the one derived for the fields and the Lagrange multipliers of the divergence constraints inside the domain.
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This velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit.
In simulations of magnetohydrodynamic (MHD) processes the violation of the divergence constraint causes severe stability problems.
The proof is based on a reformulation of the elasticity problem as a Stokes system with nonzero divergence constraint.
This ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint.
It is accomplished by the use of an iterative algorithm that enforces a divergence constraint in cells containing the interface.
We study conservation properties of Galerkin methods for the incompressible Navier Stokes equations, without the divergence constraint strongly enforced.
(2) A first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint.
Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.
It is based on a modified system in which the divergence constraint is coupled with the conservation laws by introducing a generalized Lagrange multiplier.
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