講座主題：Unconditionally energy-stable, and fully discrete finite element schemes for the Rosensweig model
專(zhuān)家姓名：董曉靖
工作單位：湘潭大學(xué)
講座時(shí)間：2026年01月20日 09:30-10:30
講座地點(diǎn)：騰訊會(huì)議：613-795-021
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
董曉靖，湘潭大學(xué)教授。主要從事不可壓縮磁流體力學(xué)高效數(shù)值算法研究。入選中國(guó)科學(xué)技術(shù)協(xié)會(huì)“第六屆青年人才托舉工程”、湖南省科技創(chuàng)新類(lèi)湖湘青年人才計(jì)劃。主持國(guó)家自然科學(xué)基金面上項(xiàng)目及青年項(xiàng)目各1項(xiàng)，作為主講人的課程《數(shù)值計(jì)算方法》分別入選省級(jí)線(xiàn)下一流課程和國(guó)家線(xiàn)下一流課程、《數(shù)值代數(shù)》入選湖南省研究生精品課程。在《Journal of Computational Physics》、《IMA Journal of Numerical Analysis》、《Science China Mathematics》、《Computer Methods in Applied Mechanics and Engineering》、《Journal of Scientific Computing》等上發(fā)表論文20余篇。
