We consider mixed finite element discretizations of two types of ferrohydrodynamics (FHD) models: the Rosensweig model and the Shliomis model. Some regularity results for the Rosensweig model are established. We prove the existence and uniqueness of the semi-discrete and fully finite element solutions of the two models, and show that the energy stability of the weak solutions is preserved exactly for all the discrete solutions. Optimal error estimates are derived. Finally, we provide numerical experiments to verify the theoretical results. This is joint work with Yongke Wu.

报告人简介：谢小平，四川大学数学学院教授（博导），四川省学术和技术带头人，教育部新世纪优秀人才，德国洪堡学者。主要从事偏微分方程数值解特别是有限元法相关研究工作，在《SIAM J. Numer. Anal.》、《SIAM J. Control Optim.》、《Numer. Math.》、《Math. Mod. Meth. Appl. S.》、《Comput. Methods Appl. Mech. Engrg》等期刊发表论文多篇。曾获教育部自然科学奖二等奖。现兼任四川省普通本科高等学校数学类教学指导委员会秘书长, 中国工业与应用数学学会油水资源数值方法专业委员会副主任委员。