| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 873 - 898 | |
| DOI | https://doi.org/10.1051/m2an/2025010 | |
| Published online | 24 March 2025 | |
Low regularity error estimates of three pressure-robust discontinuous Galerkin methods for stokes equations
1
School of Mathematics, Jiaying University, Meizhou 514015, P.R. China
2
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
* Corresponding author: szhang@udel.edu
Received:
11
July
2024
Accepted:
4
February
2025
We establish improved a priori error estimates for three pressure-robust discontinuous Galerkin (DG) approximations of the Stokes equations, assuming only minimal regularity on the exact solution. The three DG methods are the standard interior penalty DG (IPDG), the weakly over-penalized IPDG, and the conforming DG schemes. These methods are incorporated with a H(div)-conforming reconstruction operator to recover pressure-robustness. Both error estimates for the velocity in discrete energy norm and for the pressure in L2 norm are provided upto the optimal orders. The key technique relies on a trimming operator that maps the discrete divergence free test function onto the exact divergence free H1-conforming finite element space. Finally, numerical results are provided to validate the theoretical findings.
Mathematics Subject Classification: 65N15 / 65N30 / 76D07
Key words: Mixed finite element / DG method / Stokes equations / pressure-robustness / low regularity / a priori error estimate
© The authors. Published by EDP Sciences, SMAI 2025
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