Volume 37, Issue 4
Unconditional Superconvergence Analysis of an H1-Galerkin Mixed Finite Element Method for Two-Dimensional Ginzburg-Landau Equation

Dongyang Shi and Junjun Wang

10.4208/jcm.1802-m2017-0198

J. Comp. Math., 37 (2019), pp. 437-457.

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  • Abstract

An H1-Galerkin mixed finite element method (MFEM) is discussed for the two-dimensional Ginzburg-Landau equation with the bilinear element and zero order Raviart-Thomas element (Q11 + Q10 × Q01). A linearized Crank-Nicolson fully-discrete scheme is developed and a time-discrete system is introduced to split the error into two parts which are called the temporal error and the spatial error, respectively. On one hand, the regularity of the time-discrete system is deduced through the temporal error estimation. On the other hand, the superconvergent estimates of u in H1-norm and $\vec{q}$ in H(div; Ω)-norm with order O(h2 + τ2) are obtained unconditionally based on the achievement of the spatial result. At last, a numerical experiment is included to illustrate the feasibility of the proposed method. Here, h is the subdivision parameter and τ is the time step.

  • History

Published online: 2019-02

  • AMS Subject Headings

65N15, 65N30

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