何彦辰 博士 （ETH Zürich）

戴小英 研究员

Analytic regularity and hp-FEM for the stationary incompressible Navier–Stokes equations with mixed boundary conditions in polygonal domains

6月30日（周二）10:00-11:00，南楼733

The stationary incompressible Navier–Stokes equations in polygonal domains with mixed boundary conditions present substantial analytical challenges due to the interplay of corner singularities and nonlinear convection. In this talk, I will discuss a recent result establishing corner-weighted analytic regularity of velocity-pressure solutions under combinations of homogeneous Dirichlet, Neumann, and slip boundary conditions. The proof combines Kondrat'ev-type regularity theory in weighted Sobolev spaces with a novel weighted analytic estimate for the nonlinear convection term.

Based on these regularity results, I will present the analysis of a conforming mixed hp-finite element discretization which achieve exponential error-versus-work bounds. This property is confirmed by numerical experiments.