A nonconforming finite element method for the stationary Smagorinsky model

Shi, Dongyang; Li, Minghao; Li, Zhenzhen

doi:10.1016/j.amc.2019.02.012

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Solution Of the Problem By The Methods Of Mixed Finite Elements1

Introduction1

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2023

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Cited by 3 publications

(2 citation statements)

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“…One of the ways to deal with non-physical solutions is to use such formulations of the initial problem, or such systems of basic functions, which would exclude the appearance of fictitious solutions. The approach based on the application of the mixed finite element method [32][33][34] is appropriate. This method was used in [35] to calculate a plane-parallel waveguide with a non-chiral insert.…”

Section: Solution Of the Problem By The Methods Of Mixed Finite Elementsmentioning

confidence: 99%

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

Islamov¹,

Ismibayli²,

Hasanov³

et al. 2019

PIER B

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Section: Solution Of the Problem By The Methods Of Mixed Finite Elementsmentioning

confidence: 99%

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

Islamov¹,

Ismibayli²,

Hasanov³

et al. 2019

PIER B

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“…In Su et al [14], three iterative stabilized FEMs for the Smagorinsky model were proposed and analyzed. In Shi et al [15], a low‐order nonconforming mixed FEM for the Smagorinsky model was studied. In Zheng and Shang [16], a two‐step stabilized FEM for solving the Smagorinsky model was established.…”

Section: Introductionmentioning

confidence: 99%

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Yang

2023

Math Methods in App Sciences

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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.

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Modeling of Microwave Waveguide Systems of Complex Structure

Islamov

2023

Radio Engineering and Telecommunications Waveguide Systems in the Microwave Range

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A nonconforming finite element method for the stationary Smagorinsky model

Cited by 3 publications

References 20 publications

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Modeling of Microwave Waveguide Systems of Complex Structure

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