»ã±¨±êÌâ (Title)£ºH(div)-conforming HDG methods for the stress-velocity formulation of the Stokes equations and the Navier-Stokes equations£¨H(div)Ò»ÖÂÐÔHDG²½ÖèÔÚ˹ÍпË˹·½³ÌÓëÄÉά-˹ÍпË˹·½³ÌµÄÓ¦Á¦-¿ìÂʱíÊöÖеÄÀûÓã©

»ã±¨ÈË (Speaker)£ºÕÔÀûÄÈ£¨Ïã¸Û³ÇÊдóѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê05ÔÂ01ÈÕ(ÖÜÈý) 13:00-15:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÅËÏþÃô

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»ã±¨ÌáÒª£ºIn 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.