Speaker: 李步扬 (香港理工大学)
Time: 2025-11-17 16:00-17:00
Location: 1610, SIMIS
Abstract: We present recent advances in the numerical analysis of solution-driven surface evolution, spanning geometric flows, two-phase flows, and fluid-structure interactions. We report a matrix-vector framework for deriving rigorous error estimates of finite element approximations to an evolving surface driven by the solutions of PDEs on the surface itself, as well as interfaces driven by fluids on both sides or coupled with elastic structures. Our analysis addresses the interplay between errors in computing interface location and PDE solutions, providing error bounds for the problem with unknown surface/interface evolution. The rigorous error analysis allows us to understand the stability of numerical algorithms and to design more stable algorithms to preserve high-quality meshes during computations, including artificial tangential motions on the evolving surfaces and interfaces, and artificial mesh velocity which improves the bulk meshing for fluid free-boundary problems. These methods enhance the accuracy and efficiency in simulating complex interfacial dynamics.
About Speaker: 李步扬于2012年于香港城市大学获得博士学位，先后在南京大学、德国图宾根大学、香港理工大学从事教学和研究工作，现为香港理工大学应用数学系教授，计算数学期刊 Mathematics of Computation, Numerische Mathematik, SIAM Journal on Numerical Analysis, IMA Journal of Numerical Analysis 编委。主要研究领域为偏微分方程的科学计算和数值分析，包括几何曲率流、流体自由边界问题、流固耦合自由界面问题的数值方法及数值分析，非线性色散和波动方程不光滑解的数值计算，等等。曾入选香港研资局研究学者奖，国家自然科学基金青年科学基金项目A类。
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