报告题目：New error analysis of charge-conservative finite element methods for stationary inductionless MHD equations

主讲人：张晓迪

单位：郑州大学

时间：5月6日8:40-10:40

腾讯ID：999-127-918

密码：202305

摘要：In this paper, we present a new error analysis of a class of charge-conservative finite element methods for stationary inductionless magnetohydrodynamics (MHD) equations. The methods use the standard inf-sup stable Mini/Taylor—Hood pairs to discretize the velocity and pressure, and the Raviart--Thomas face element for solving the current density. Due to the strong coupling of the system and the pollution of the lower-order Raviart--Thomas face approximation in analysis, the existing analysis is not optimal. In terms of a mixed Poisson projection and the corresponding estimate in negative norms, we establish new and optimal error estimates. In particular, we prove that the method with the lowest-order Raviart--Thomas face element and Mini element provides the optimal accuracy for the velocity in $\boldsymbol{L}^{2}$-norm, and the method with the lowest-order Raviart--Thomas face element and $\boldsymbol{P}_2-P_1$ Taylor-Hood element supplies the optimal accuracy for the velocity in $\boldsymbol{H}^{1}$-norm and the pressure in $L^{2}$-norm. Furthermore, we propose a simple recovery technique to obtain a new numerical current density of one order higher accuracy by re-solving a mixed Poisson equation. Numerical results are provided to verify the theoretical analysis.

简介：张晓迪，郑州大学河南省大数据研究院讲师。2016年本科毕业于陕西师范大学，2021年博士毕业于中国科学院数学与系统科学研究院，2021年7月至今在郑州大学工作。主要从事偏微分方程数值解研究，研究领域为有限元方法和磁流体计算，在CMAME、JSC、CNSNS、JCM和CAMWA等杂志上共发表8篇论文。目前主持国家自然科学基金青年基金一项，中国博士后基金面上基金一项和教育部重点实验室开放课题一项。