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Finite element approximation of a sixth order nonlinear degenerate parabolic equation

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Summary.

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation where generically for any given In addition to showing well-posedness of our approximation, we prove convergence in space dimensions $d \leq 3$. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College, London, SW7 2AZ, UK

    John W. Barrett, Stephen Langdon & Robert Nürnberg

  2. Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK

    Stephen Langdon

Authors
  1. John W. Barrett
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  2. Stephen Langdon
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  3. Robert Nürnberg
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Correspondence to John W. Barrett.

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Mathematics Subject Classification (2000): 65M60, 65M12, 35K55, 35K65, 35K35

Supported by the EPSRC, U.K. through grant GR/M29689.

Supported by the EPSRC, and by the DAAD through a Doktorandenstipendium

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Barrett, J., Langdon, S. & Nürnberg, R. Finite element approximation of a sixth order nonlinear degenerate parabolic equation. Numer. Math. 96, 401–434 (2004). https://doi.org/10.1007/s00211-003-0479-4

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  • DOI: https://doi.org/10.1007/s00211-003-0479-4

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