讲座主题：Unconditionally energy-stable, and fully discrete finite element schemes for the Rosensweig model

专家姓名：董晓靖

工作单位：湘潭大学

讲座时间：2026年01月20日 09:30-10:30

讲座地点：腾讯会议：613-795-021

主办单位：烟台大学数学与信息科学学院

内容摘要：

Ferrohydrodynamics (FHD) describes the motion of a magnetic fluid, usually called a ferrofluid. A ferrofluid is a stable colloidal fluid consisting of nanoscale ferromagnetic particles suspended in a carrier fluid. A colloidal ferrofluid can keep magnetization and fluidity under the action of an external magnetic field.The constitutive equation we consider, proposed by Rosensweig, models fluid dynamics, spins of ferromagnetic particles, magnetic polarization, and a magnetic induction field. The corresponding model incorporates the Navier-Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equation. In this talk, we propose linear, unconditionally energy-stable, and fully discrete finite element schemes for the model. We obtain the existence and uniqueness of the numerical solutions by the Leray-Schauder fixed point theorem, and prove the unconditional convergence through the Aubin-Lions-Simon lemma. Numerical experiments verify the effectiveness and accuracy of the schemes, and simulate the controllability of the magnetic fluid driven by an applied magnetic field.

主讲人介绍：

董晓靖，湘潭大学教授。主要从事不可压缩磁流体力学高效数值算法研究。入选中国科学技术协会“第六届青年人才托举工程”、湖南省科技创新类湖湘青年人才计划。主持国家自然科学基金面上项目及青年项目各1项，作为主讲人的课程《数值计算方法》分别入选省级线下一流课程和国家线下一流课程、《数值代数》入选湖南省研究生精品课程。在《Journal of Computational Physics》、《IMA Journal of Numerical Analysis》、《Science China Mathematics》、《Computer Methods in Applied Mechanics and Engineering》、《Journal of Scientific Computing》等上发表论文20余篇。