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Error estimates of a two-grid penalty finite element method for the Smagorinsky model
  • Yun-Bo Yang
Yun-Bo Yang
Yunnan Normal University

Corresponding Author:[email protected]

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Abstract

In the paper, we consider the penalty finite element methods (FEMs) for the stationary Smagorinsky model. Firstly, a one-grid penalty FEM is proposed and analyzed. Since this method is nonlinear, a novel linearized iteration scheme is derived for solving it. We also derived the stability and convergence of numerical solutions for this iteration scheme. Furthermore, a two-grid penalty FEM is developed for Smagorinsky model. Under $\varepsilon<

Peer review status:ACCEPTED

19 Jun 2022Submitted to Mathematical Methods in the Applied Sciences
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20 Jun 2022Submission Checks Completed
20 Jun 2022Assigned to Editor
28 Jun 2022Reviewer(s) Assigned
02 Nov 2022Review(s) Completed, Editorial Evaluation Pending
03 Nov 2022Editorial Decision: Revise Major
20 Feb 20231st Revision Received
21 Feb 2023Assigned to Editor
21 Feb 2023Submission Checks Completed
21 Feb 2023Review(s) Completed, Editorial Evaluation Pending
21 Feb 2023Reviewer(s) Assigned
11 Apr 2023Editorial Decision: Revise Major
10 Jun 20232nd Revision Received
14 Jun 2023Assigned to Editor
14 Jun 2023Submission Checks Completed
14 Jun 2023Review(s) Completed, Editorial Evaluation Pending
21 Jun 2023Reviewer(s) Assigned
08 Jul 2023Editorial Decision: Accept