Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
arXiv:1304.6908 · doi:10.1016/j.jcp.2013.08.005
Abstract
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 -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.
27 pages
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