In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral
grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field
problem.
The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations.
In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition
between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual
grid.
Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations
of the electromagnetic field.
