In this article, we introduce and analyze arbitrary-order, locally conservative hybrid discontinuous Galkerin methods for linearized Navier–Stokes equations. The unknowns of the global system are reduced to trace variables on the skeleton of a triangulation and the average of pressure on each cell via embedded static condensation. We prove that the lifting operator associated with trace variables is injective for any polynomial degree. This generalizes the result in (Y. Jeon and E.-J. Park, Numerische Mathematik 123 , no. 1, pp. 97–119), where quadratic and cubic rectangular elements are analyzed. Moreover, optimal error estimates in the energy norm are obtained by introducing nonstandard projection operators for the hybrid DG method. Several numerical results are presented to show the performance of the algorithm and to validate the theory developed in the article.
|Number of pages||25|
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Published - 2023 Jan|
Bibliographical noteFunding Information:
This work was supported by National Research Foundation of Korea under grants NRF‐2017R1D1A1B03035708 and NRF‐2020R1F1A1A01076151 (Dongwook Shin), NRF‐2018R1D1A1A09082082 (Youngmok Jeon), and NRF‐2015R1A5A1009350 and NRF‐2019R1A2C2090021 (Eun‐Jae Park). Funding information
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics