Volume 57, Number 1, January-February 2023
|Page(s)||271 - 297|
|Published online||03 February 2023|
Analysis of an HDG method for the Navier–Stokes equations with Dirac measures
School of Mathematics and information sciences, Guangzhou University, Guangzhou, Guangdong, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 5 September 2022
In two dimensions, we analyze a hybridized discontinuous Galerkin (HDG) method for the Navier–Stokes equations with Dirac measures. The approximate velocity field obtained by the HDG method is shown to be pointwise divergence-free and H(div)-conforming. Under a smallness assumption on the continuous and discrete solutions, a posteriori error estimator, that provides an upper bound for the L2-norm in the velocity, is proposed in the convex domain. In the polygonal domain, reliable and efficient a posteriori error estimator for the W1,q-seminorm in the velocity and Lq-norm in the pressure is also proved. Finally, a Banach’s fixed point iteration method and an adaptive HDG algorithm are introduced to solve the discrete system and show the performance of the obtained a posteriori error estimators.
Mathematics Subject Classification: 65J15 / 65N50 / 65N15 / 76D05
Key words: Hybridized discontinuous Galerkin method / a posteriori error estimate / Navier–Stokes equation / divergence-free / Dirac
© The authors. Published by EDP Sciences, SMAI 2023
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