2018/06/24 by Meng Li, Li, Meng, Dongyang Shi +3 · 1 citation
Engineering · Mathematics · #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1806.09157
openalex publication_date 2018/06/24 · openalex created_date 2018/07/10 · openalex updated_date 2026/08/01
In this paper, a linearized Crank-Nicolson Galerkin finite element method (FEM) for generalized Ginzburg-Landau equation (GLE) is considered, in which, the difference method in time and the standard Galerkin FEM are employed. Based on the linearized Crank-Nicolson difference method in time and the standard Galerkin finite element method with bilinear element in space, the time-discrete and space-time discrete systems are both constructed. We focus on a rigorous analysis and consideration of unconditional superconvergence error estimates of the discrete schemes. Firstly, by virtue of the temporal error results, the regularity for the time-discrete system is presented. Secondly, the classical Ritz projection is used to obtain the spatial error with order O(h2) in the sense of L2-norm. Thanks to the relationship between the Ritz projection and the interpolated projection, the superclose estimate with order O(τ2 + h2) in the sense of H1-norm is derived. Thirdly, it follows from the interpolated postprocessing technique that the global superconvergence result is deduced. Finally, some numerical results are provided to confirm the theoretical analysis.