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An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • François Bouchon

    (Université Blaise-Pascal (Clermont-Ferrand 2), Laboratoire de Mathématiques, UMR CNRS 6620)

  • Gunther H. Peichl

    (Karl-Franzens-University Graz, Institute for Mathematics and Scientific Computing)

Abstract

A finite difference scheme for the heat equation with mixed boundary conditions on a moving domain is presented. We use an immersed interface technique to discretize the Neumann condition and the Shortley–Weller approximation for the Dirichlet condition. Monotonicity of the discretized parabolic operator is established. Numerical results illustrate the feasibility of the approach.

Suggested Citation

  • François Bouchon & Gunther H. Peichl, 2010. "An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 181-189, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_18
    DOI: 10.1007/978-3-642-11795-4_18
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