Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations
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Date
2019-08-30
Authors
Kirk, Keegan L.A.
Rhebergen, Sander
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin
method for the stationary form of the Navier-Stokes problem proposed in (J Sci Comput, 76(3):1484{
1501, 2018). This scheme was shown to result in an approximate velocity eld that is pointwise
divergence-free and divergence-conforming. As a consequence we show that the velocity error estimate
is independent of the pressure. Furthermore, we show that estimates for both the velocity
and pressure are optimal. Numerical examples demonstrate pressure-robustness and optimality of
the scheme.
Description
Keywords
Navier-Stokes, finite element method, hybridized, discontinuous Galerkin, pressure-robust