Discrete Versions of Stokes’ Theorem Based on Families of Weights on Hypercubes
This paper generalizes to higher dimensions some algorithms that we developed in [1,2,3] using a discrete version of Green’s theorem. More precisely, we present discrete versions of Stokes’ theorem and Poincaré lemma based on families of weights on hypercubes. Our approach is similar to that of Mansfield and Hydon  where they start with a concept of difference forms to develop their discrete version of Stokes’ theorem. Various applications are also given.
KeywordsDiscrete Stokes’ theorem Poincaré lemma hypercube
- 3.Lacasse, A.: Contributions à l’analyse de figures discrètes en dimension quelconque. PhD thesis, Université du Québec à Montréal (September 2008)Google Scholar
- 4.Mansfield, E.L., Hydon, P.E.: Difference forms. Found. Comp. Math.(2007), http://personal.maths.surrey.ac.uk/st/P.Hydon/
- 7.González-Díaz, R., Real, P.: On the cohomology of 3D digital images. Discrete Appl. Math. 147(2-3), 245–263 (2005)Google Scholar