A linearized Crank-Nicolson-Galerkin FEM for the time-dependent Ginzburg-Landau equations under the temporal gauge

作者：Yang, Chaoxia^*

来源：Numerical Methods for Partial Differential Equations, 2014, 30(4): 1279-1290.

DOI：10.1002/num.21869

• degenerate
• convergence rate
• Crank-Nicolson
• Ginzburg-Landau
• temporal gauge
• finite element

We propose a decoupled and linearized fully discrete finite element method (FEM) for the time-dependent Ginzburg-Landau equations under the temporal gauge, where a Crank-Nicolson scheme is used for the time discretization. By carefully designing the time-discretization scheme, we manage to prove the convergence rate O(tau 2+hr), where tau is the time-step size and r is the degree of the finite element space. Due to the degeneracy of the problem, the convergence rate in the spatial direction is one order lower than the optimal convergence rate of FEMs for parabolic equations. Numerical tests are provided to support our error analysis.

• 出版日期2014-7
• 单位中国石油大学（北京）