Premium
The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
Author(s) -
Barrett John W.,
Garcke Harald,
Nürnberg Robert
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20637
Subject(s) - mathematics , parametric statistics , parametric equation , finite element method , nonlinear system , planar , basis (linear algebra) , surface (topology) , partial differential equation , plane (geometry) , mathematical analysis , geometry , computer science , statistics , physics , computer graphics (images) , thermodynamics , quantum mechanics
On the basis of our previous work, 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. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010