 
Summary: Numerische Mathematik manuscript No.
(will be inserted by the editor)
A nite dierence scheme on a non
commutative group
Yves Achdou 1 and Nicoletta Tchou 2
1 INSA Rennes and Laboratoire ASCI, CNRS, Orsay
2 IRMAR, Universite de Rennes 1, Campus de Beaulieu, 35 000 Rennes, France,
email: nicoletta.tchou@univrennes1.fr
The date of receipt and acceptance will be inserted by the editor
Summary We propose and analyze a nite dierence scheme for
the Kohn Laplacian operator associated with the Heisenberg group,
which is a degenerate elliptic operator of Hormander type. We give
a complete analysis for a periodic problem in a cube. In particular,
we prove a discrete PoincareWiertinger inequality which yields the
stability. Numerical tests are presented.
1 Introduction
We consider an important model homogeneous group, namely the so
called Heisenberg group, and the invariant operator associated with
the Heisenberg group, i.e. the Kohn Laplacian operator H (see [9,
8,4{7] for the properties of the operator). As explained in Stein (see
