Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg–Landau functionals

The Sobolev gradient technique has been discussed previously in this journal as an efficient method for finding energy minima of certain Ginzburg–Landau type functionals [S. Sial, J. Neuberger, T. Lookman, A. Saxena, Energy minimization using Sobolev gradients: application to phase separation and ordering, J. Comput. Phys. 189 (2003) 88–97]. In this article a Sobolev gradient method for the related time evolution is discussed.