Finite element approximation of a fourth order nonlinear degenerate parabolic equation

Summary.

We consider a fully practical finite element approximation of the fourth order nonlinear degenerate parabolic equation $u_{t} + \nabla .( b(u) \nabla \delta u) = 0,$where generically $b(u) := |u|^p$ for any given $p \in (0, \infty)$. An iterative scheme for solving the resulting nonlinear discrete system is analysed. In addition to showing well-posedness of our approximation, we prove convergence in one space dimension. Finally some numerical experiments are presented.