Unconditional superconvergent analysis of a linearized finite element method for Ginzburg-Landau equation

摘要

In this paper, unconditional superconvergent estimate with a Galerkin finite element method (FEM) is presented for Ginzburg-Landau equation by conforming bilinear FE, while all previous works require certain time-step restrictions. First of all, a time-discrete system is introduced, with which the error function is split into a temporal error and a spatial error. On one hand, the regularity of the time-discrete system is deduced with a rigorous analysis. On the other hand, the error between the numerical solution and the solution of the time-discrete system is derived tau-independently with order O(h(2) + h tau), where h is the subdivision parameter and tau, the time step. Then, the unconditional superclose result of order O(h(2) + tau) in the H-1-norm is deduced directly based on the above estimates. Furthermore, the global superconvergent result is obtained through the interpolated postprocessing technique. At last, numerical results are provided to confirm the theoretical analysis. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.