We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ∇.(b(u) δ 22u), where generically b(u): = |u|γ for any given γ ∈ (0, ∞). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ≤ 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.

Finite element approximation of a sixth order nonlinear degenerate parabolic equation / Barrett, J. W.; Langdon, S.; Nürnberg, R.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 96:3(2004), pp. 401-434. [10.1007/s00211-003-0479-4]

Finite element approximation of a sixth order nonlinear degenerate parabolic equation

Nürnberg R.
2004

Abstract

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ∇.(b(u) δ 22u), where generically b(u): = |u|γ for any given γ ∈ (0, ∞). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ≤ 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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Barrett, J. W.; Langdon, S.; Nürnberg, R.
Finite element approximation of a sixth order nonlinear degenerate parabolic equation / Barrett, J. W.; Langdon, S.; Nürnberg, R.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 96:3(2004), pp. 401-434. [10.1007/s00211-003-0479-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/283499
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