Quantitative towers in finite difference calculus approximating the continuum. (4th December 2020)

• Record Type: Journal Article
• Authors: Lawrence, R; Ranade, N; Sullivan, D
• Is Part Of: Quarterly journal of mathematics. Volume 72:Part 1/2(2021)
• Page Start: 515
• Page End: 545
• Publication Date: 2020-12-04
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/haaa060
• Languages: English
• ISSNs: 0033-5606

Abstract

Abstract: Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like $\partial$, d and '*' which are used to describe many nonlinear problems. The point of this paper is to construct consistent direct and inverse systems of finite dimensional approximations to these structures and to calculate combinatorially how these finite dimensional models differ from their continuum idealizations. In a Euclidean background, there is an explicit answer which is natural statistically .