Finite element approximation of a fourth order nonlinear degenerate parabolic equation.

Blowey, J.F.; Barrett, J.W.; Garcke, H.

Abstract

We consider a fully practical finite element approximation of the fourth order nonlinear degenerate parabolic equation ut+∇.(b(u)∇δu)=0, where generically b(u):=|u|p for any given p∈(0,∞). 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.

Citation

Blowey, J., Barrett, J., & Garcke, H. (1998). Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Numerische Mathematik, 80(4), 525-556. https://doi.org/10.1007/s002110050377

• Journal Article Type: Article
• Publication Date: 1998
• Journal: Numerische Mathematik
• Print ISSN: 0029-599X
• Electronic ISSN: 0945-3245
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 80
• Issue: 4
• Pages: 525-556
• DOI: https://doi.org/10.1007/s002110050377
• Public URL: https://durham-repository.worktribe.com/output/1599375