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Quasi-uniform and unconditional superconvergence analysis of Ciarlet–Raviart scheme for the fourth order singularly perturbed Bi-wave problem modeling d-wave superconductors
Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2021-01-11 , DOI: 10.1016/j.amc.2020.125924
Yanmi Wu , Dongyang Shi

In this paper, two implicit Backward Euler (BE) and Crank-Nicolson (CN) formulas of Ciarlet–Raviart mixed finite element method (FEM) are presented for the fourth order time-dependent singularly perturbed Bi-wave problem arising as a time-dependent version of Ginzburg-Landau-type model for d-wave superconductors by the bilinear element. The well-posedness of the weak solution and the approximation solutions of the considered problem are proved through Faedo-Galerkin technique and Brouwer fixed point theorem, respectively. The quasi-uniform and unconditional superconvergent estimates of O(h2+τ) and O(h2+τ2)(h, the spatial parameter, and τ, the time step) in the broken H1- norm are obtained for the above formulas independent of the negative powers of the perturbation parameter δ. Some numerical results are provided to illustrate our theoretical analysis.



中文翻译:

四阶奇摄动双波问题建模的Ciarlet-Raviart格式的拟均匀无条件超收敛分析 d波超导体

本文针对四阶随时间变化的时间相关奇异摄动双波问题,提出了Ciarlet-Raviart混合有限元方法(FEM)的两个隐式Backward Euler(BE)和Crank-Nicolson(CN)公式。 Ginzburg-Landau型模型的从属版本 d双线性单元构成的超波。分别通过Faedo-Galerkin技术和Brouwer不动点定理证明了弱解的适定性和所考虑问题的逼近解。的准一致和无条件超收敛估计ØH2+τØH2+τ2H 空间参数,以及 τ 时间步)在破碎 H1个-以上公式的范数与扰动参数的负幂无关 δ。提供一些数值结果来说明我们的理论分析。

更新日期:2021-01-11
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