Affiliation:
1. Department of Mathematics Yunnan Normal University Kunming China
2. Yunnan Key Laboratory of Modern Analytical Mathematics and Applications Yunnan Normal University Kunming China
3. Key Laboratory of Complex System Modeling and Application for Universities in Yunnan Yunnan Normal University Kunming China
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
, this method consist of solving a nonlinear Smagorinsky model by the one‐grid penalty FEM with the proposed linearized iteration scheme on a coarse mesh with mesh width
and then solving a linearized Smagorinsky model based on the Newton iteration on a fine mesh with mesh width
, respectively. Stability and error estimates of numerical solutions for two‐grid penalty FEM are presented. Finally, some numerical tests are provided to confirm the theoretical analysis and the effectiveness of the developed methods.
Funder
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics
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