Numerical approximation of time evolution related to GinzburgLandau functionals using weighted Sobolev gradients
Sobolev gradients have been discussed in Sial etal. (2003) as a method for energy minimization related to GinzburgLandau functionals. In this article, a weighted Sobolev gradient approach for the time evolution of a GinzburgLandau functional is presented for different values of ? ? . A comparison is given between the weighted and unweighted Sobolev gradients in a finite element setting. It is seen that for small values of ? ? , the weighted Sobolev gradient method becomes more and more efficient compared to using the unweighted Sobolev gradient. A comparison with Newtons method is given where the failure of Newtons method is demonstrated for a test problem.
ginzburglandau functional sobolev gradient finite-element setting steepest descent