Barrett, John W. and Garcke, Harald and Nürnberg, Robert
The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute.
Numer. Methods Partial Differential Equations 27 (1), pp. 1-30.
Based on earlier work by the authors, in this paper we introduce novel fully
discrete, fully practical parametric finite element approximations for geometric evolution
equations of curves in the plane. The fully implicit approximations are unconditionally
stable and intrinsically equidistribute the vertices at each time level.
We present iterative solution methods for the systems of nonlinear equations arising
at each time level and present several numerical results. The ideas easily generalize
to the evolution of curve networks and to anisotropic surface energies.
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||parametric finite elements, equidistributed polygonal meshes, curve evolution, anisotropy, networks of curves, gradient flows|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Partially|
|Deposited On:||23 Mar 2010 08:13|
|Last Modified:||20 Jul 2011 22:23|