报告时间：2022/10/25 13:30-15:00
重复周期：2022/09/13-2022/12/27 10:00-16:00, 每周 (周二)
报告人：高华东 副教授
腾讯会议：932-7827-6364
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报告摘要：This talk is concerned with new error analysis of a lowest-order backward Euler Galerkin-mixed finite element method for the time-dependent Ginzburg--Landau equations. The method is based on a commonly-used non-uniform approximations, in which linear Lagrange element, the lowest order Nedelec edge element and Raviart--Thomas face element are used for the order parameter $\psi$, the magnetic field $curl \mathbf{A}$ and the magnetic potential $\mathbf{A}$, respectively. This mixed method has been widely used in practical simulations due to its low cost and ease of implementation. In the Ginzburg-Landau model, the order parameter $\psi$ is the most important variable, which indicates the state of the superconductor. An important feature of the method is the inconsistency of the approximation orders. A crucial question is how the first-order approximation of $(curl \mathbf{A}, \mathbf{A})$ influences the accuracy of $\psi_h$. The main purpose is to establish the second-order accuracy for the order parameter in spatial direction, although the accuracy for $curl \mathbf{A}, \mathbf{A}$ is in the first order only. Previous analysis only gave the first order convergence for all three variables due to certain artificial pollution involved in analysis. Our analysis is based on a nonstandard quasi-projection for $\psi$ and the corresponding more precise estimates, including in $H^{-1}$-norm. With the quasi-projection, we prove that the lower-order approximation to $curl \mathbf{A}, \mathbf{A}$ does not pollute the accuracy of $\psi_h$. Our numerical experiments confirm the optimal convergence of $\psi_h$. The approach can be extended to many other multi-physics models.
报告人简介：高华东博士，华中科技大学数学与统计学院副教授. 研究方向包括数值分析: 微分方程数值解, 有限元方法与差分方法, 尤其是对非线性抛物问题的数值求解与分析; 数学建模与计算物理: 多孔介质中热和水汽的传导流动, 计算超导现象, 计算微磁学, 计算电热学。主持多项国家自然科学基金，已发表论文二十余篇，其中包括SIAM Journal on Numerical Analysis, Numerische Mathematik，Journal of Computational Physics等。
邀请人：杜锐