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.
2004-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
