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Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
- Publication Year :
- 2013
-
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 $\star$-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.<br />Comment: 27 pages
- Subjects :
- Mathematics - Numerical Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1304.6908
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jcp.2013.08.005