报告题目 (Title)：H(div)-conforming HDG methods for the stress-velocity formulation of the Stokes equations and the Navier-Stokes equations（H(div)一致性HDG方法在斯托克斯方程与纳维-斯托克斯方程的应力-速度表述中的应用）

报告人 (Speaker)：赵利娜（香港城市大学）

报告时间 (Time)：2024年05月01日(周三) 13:00-15:00

报告地点 (Place)：校本部F309

邀请人(Inviter)：潘晓敏

主办部门：理学院数学系

报告摘要：In this talk we present a pressure-robust and superconvergent HDG method in stress-velocity formulation for the Stokes equations and the Navier-Stokes equations with strongly symmetric stress. The stress and velocity are approximated using piecewise polynomial space of order k and H(div)-conforming space of order k+1, respectively, where k is the polynomial order. In contrast, the tangential trace of the velocity is approximated using piecewise polynomials of order k. The discrete H^1-stability is established for the discrete solution. The proposed formulation yields divergence-free velocity, but causes difficulties for the derivation of the pressure-independent error estimate given that the pressure variable is not employed explicitly in the discrete formulation. This difficulty can be overcome by observing that the L^2 projection to the stress space has a nice commuting property. Moreover, superconvergence for velocity in discrete H^1-norm is obtained, with regard to the degrees of freedom of the globally coupled unknowns. Then the convergence of the discrete solution to the weak solution for the Navier-Stokes equations via the compactness argument is rigorously analyzed under minimal regularity assumption. The strong convergence for velocity and stress is proved. Importantly, the strong convergence for velocity in discrete H^1-norm is achieved. Several numerical experiments are carried out to confirm the proposed theories.