TY - JOUR
T1 - Quantitative towers in finite difference calculus approximating the continuum
AU - Lawrence, R.
AU - Ranade, N.
AU - Sullivan, D.
N1 - Publisher Copyright: © 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
PY - 2021/6/1
Y1 - 2021/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85108981348&partnerID=8YFLogxK
U2 - 10.1093/qmath/haaa060
DO - 10.1093/qmath/haaa060
M3 - مقالة
SN - 0033-5606
VL - 72
SP - 515
EP - 545
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1-2
ER -