Distinguished Lecture——Robust Discretization of Surface PDEs
报告人：Ricardo H. Nochetto (University of Maryland College Park)
时间：2026-06-12 15:10-16:10
地点：智华楼四元厅
报告摘要：
Consider hypersurfaces of class $C^2$ embedded in $R^d$. We first discuss a sharp parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the surface heat equation that adds a novel $L^2$-type stabilization to the time derivative. This yields uniform well-posedness, parabolic quasi-best approximation, optimal order-regularity error estimates, and robust conditioning with respect to time step. We next present a reformulation of the stationary and transient surface Stokes equations in terms of a non-symmetric indefinite elliptic problem governed by two Laplacians and further discretized by ParamatericFEM or TraceFEM. We prove well posedness, quasi-best approximation in a robust mesh-dependent norm for any polynomial degree, as well as optimal order-regularity error estimates for both velocity and pressure. This entails a sufficiently small mesh size that solely depends on the Weingarten map and circumvents the usual discrete inf-sup condition. The first problem is joint with L. Bouck, V. Yushutin and M. Shakipov, while the second one is joint with M. Shakipov.
报告人摘要：
Ricardo H. Nochetto is a Professor in the Department of Mathematics and the Institute for Physical Science and Technology (IPST) at the University of Maryland, College Park. As an internationally recognized authority in numerical analysis and computational mathematics, his foundational research comprehensively encompasses the foundations of finite element and virtual element methods (FEMs and VEMs), fractional diffusion, nonlinear elasticity, fully nonlinear PDEs, free boundary problems, complex fluids, and surface PDEs. In recognition of his profound impact on the field, Professor Nochetto was an invited speaker at the International Congress of Mathematicians (ICM 2010) and a plenary speaker at the International Congress on Industrial and Applied Mathematics (ICIAM 2015). He is a recipient of the Giovanni Sacchi Landriani Prize and an elected Fellow of both the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).
