  This paper introduces the basic concepts for physics-compatible
discretization techniques. The paper gives a clear distinction between vectors
and forms. Based on the difference between forms and pseudo-forms and the
$\star$-operator which switches between the two, a dual grid description and a
single grid description are presented. The dual grid method resembles a
staggered finite volume method, whereas the single grid approach shows a strong
resemblance with a finite element method. Both approaches are compared for the
Poisson equation for volume forms.
