报告人：谢小平，四川大学

报告题目：Stability Analysis of Monolithic Globally Divergence-Free ALE-HDG Methods for Fluid-Structure Interaction

时间：2026.4.19上午10:00-11:00

地点：数学楼2-3会议室

报告摘要：

We propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the backward Euler method to both the non-conservative and conservative formulations. For the spatial discretization, we adopt arbitrary order hybridizable discontinuous Galerkin (HDG) methods for the incompressible Navier-Stokes and linear elasticity equations, and a continuous Galerkin (CG) method for the fluid mesh movement. We derive stability results for both the temporal semi-discretization and the fully discretization, and show that the velocity approximations of the fully discrete schemes are globally divergence-free. Several numerical experiments are performed to verify the performance of the proposed methods.

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.