Discrete Poincaré lemma
نویسندگان
چکیده
منابع مشابه
The Poincaré Lemma in Subriemannian Geometry
This work is a short, self-contained introduction to subriemannian geometry with special emphasis on Chow’s Theorem. As an application, a regularity result for the the Poincaré Lemma is presented. At the beginning, the definitions of a subriemannian geometry, horizontal vectorfields and horizontal curves are given. Then the question arises: Can any two points be connected by a horizontal curve?...
متن کاملA Discrete Farkas Lemma
Given A ∈ Zm×n and b ∈ Zm, we consider the issue of existence of a nonnegative integral solution x ∈ Nn to the system of linear equations Ax = b. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in Rn and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.
متن کاملPoincaré ’ S Lemma on Some Non - Euclidean Structures
In this paper we prove the Poincaré lemma on some n-dimensional corank 1 sub-Riemannian structures, formulating the (n−1)n(n +3n−2) 8 necessarily and sufficiently ’curl-vanishing’ compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. Our proof is based on a Poincaré lemma stated on Riemannian manifolds and a suitable Cesàro-Volterra...
متن کاملDiscrete Poincaré lemma
This paper proves a discrete analogue of the Poincaré lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone operator, p :Ck(K)→ Ck+1(K), as the geometric cone of a simplex cannot, in general, be interpreted as a chain in the simplicial complex. The corresponding cocone operator H :Ck(K)→ Ck−1(K) can be shown ...
متن کاملDiscrete Sobolev-Poincaré Inequalities for Voronoi Finite Volume Approximations
We prove a discrete Sobolev-Poincaré inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev’s integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 2005
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2004.09.035