Discrete Versions of Stokes’ Theorem Based on Families of Weights on Hypercubes

Abstract

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 [4] where they start with a concept of difference forms to develop their discrete version of Stokes' theorem. Various applications are also given.