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A finite difference scheme on a non commutative group

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Summary.

We propose and analyze a finite difference scheme for the Kohn Laplacian operator associated with the Heisenberg group, which is a degenerate elliptic operator of Hörmander type. We give a complete analysis for a periodic problem in a cube. In particular, we prove a discrete Poincaré-Wiertinger inequality which yields the stability. Numerical tests are presented.

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Authors and Affiliations

  1. INSA Rennes, 20 Av des Buttes de Coesmes, 35043 Rennes, France , , , , , , FR

    Yves Achdou

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 000 Rennes, France; e-mail: nicoletta.tchou@univ-rennes1.fr , , , , , , FR

    Nicoletta Tchou

Authors
  1. Yves Achdou
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  2. Nicoletta Tchou
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Received June 1, 1999 / Revised version received June 7, 2000 / Published online March 20, 2001

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Achdou, Y., Tchou, N. A finite difference scheme on a non commutative group. Numer. Math. 89, 401–424 (2001). https://doi.org/10.1007/PL00005472

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  • DOI: https://doi.org/10.1007/PL00005472

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