A finite difference scheme on a non commutative group

Authors
Achdou, Y Tchou, N
Citation
Y. Achdou et N. Tchou, A finite difference scheme on a non commutative group, NUMER MATH, 89(3), 2001, pp. 401-424
Citations number
12
Categorie Soggetti
Mathematics
Journal title
NUMERISCHE MATHEMATIK
ISSN journal
0029599X → ACNP
Volume
89
Issue
3
Year of publication
2001
Pages
401 - 424
Database
ISI
SICI code
0029-599X(200109)89:3<401:AFDSOA>2.0.ZU;2-6
Abstract
We propose and analyze a finite difference scheme for the Kohn Laplacian op erator associated with the Heisenberg group, which is a degenerate elliptic operator of Hormander type. We give a complete analysis for a periodic pro blem in a cube. In particular, we prove a discrete Poincare-Wiertinger ineq uality which yields the stability. Numerical tests are presented.