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

2022/04/07 by Chen, Gang, Xie, Xiaoping
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2204.03246

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 P_k/P_k-1 (k≥1) discontinuous finite element combination for the velocity and pressure approximations 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. 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.

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