Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations

DOI10.1007/S11425-022-2077-7arXiv2204.03246OpenAlexW4381857245MaRDI QIDQ6395921

Publication date: 7 April 2022

Abstract: This paper analyzes 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

m a t h c a l P_{k} / m a t h c a l P_{k - 1}

(k g e q 1)

discontinuous finite element combination for the velocity and pressure approximations in the interior of elements, and piecewise

m a t h c a l P_{k} / m a t h c a l P_{k}

for the trace approximations of the velocity and pressure on the inter-element boundaries. It is shown 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.

Full work available at URL: https://doi.org/10.1007/s11425-022-2077-7

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)