摘要
In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the P_(k)/P_(k-1)(k≥1)discontinuous finite element combination for the velocity and pressure approximations in the interior of elements,piecewise Pm(m=k,k-1)for the velocity gradient approximation in the interior of elements,and piecewise P_(k)/P_(k) for the trace approximations of the velocity and pressure on the inter-element boundaries.We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size.Based on the derived discrete HDG Sobolev embedding properties,optimal error estimates are obtained.Numerical experiments are performed to verify the theoretical analysis.
基金
supported by National Natural Science Foundation of China(Grant Nos.12171341 and 11801063)
supported by National Natural Science Foundation of China(Grant Nos.12171340 and 11771312)
the Fundamental Research Funds for the Central Universities(Grant No.YJ202030)。