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On Discrete Stokes and Navier—Stokes Equations in the Plane

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Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

The main goal of the paper is to apply the theory of discrete analytic functions to the solution of Dirichlet problems for the Stokes and Navier—Stokes equations, respectively. The Cauchy—Riemann operator will be approximated by certain finite difference operators. Approximations of the classical T-operator as well as for the Bergman projections are constructed in such a way that the algebraic properties of the operators from complex function theory remain valid. This is used to approximate the solutions to the boundary value problems by adapted finite difference schemes.

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Author information

Authors and Affiliations

  1. Institut für Mathematik/Physik, Bauhaus-Universität Weimar, Coudraystr. 13 B, 99423, Weimar, Germany

    Klaus Gürlebeck & Angela Hommel

Authors
  1. Klaus Gürlebeck
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  2. Angela Hommel
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Gürlebeck, K., Hommel, A. (2004). On Discrete Stokes and Navier—Stokes Equations in the Plane. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_3

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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