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A NEW STABILIZED SUBGRID EDDY VISCOSITY method BASED ON pressure projection AND EXTRAPOLATED TRAPEZOIDAL RULE FOR THE TRANSIENT NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 2011年第4期29卷 415-440页

作者： Minfu Feng Yanhong Bai Yinnian He Yanmei Qin School of Mathematics Sichuan University Chengdu 610064 China Department of Mathematics Taiyuan Teachers College Taiyuan 030012 China Faculty of Science Xian Jiaotong University Xian 710049 China Key Laboratory of Numberical Simulation of Sichuan Province Neijiang 641112 China

We consider a new subgrid eddy viscosity method based on pressure projection and extrapolated trapezoidal rule for the transient Navier-Stokes equations by using lowest equal-order pair of finite elements. The scheme stabilizes convection dominated problems and ameliorates the restrictive inf-sup compatibility stability. It has some attractive fea- tures including parameter free for the pressure stabilized term and calculations required for higher order derivatives. Moreover, it requires only the solutions of the linear system arising from an Oseen problem per time step and has second order temporal accuracy. The method achieves optimal accuracy with respect to solution regularity.

关键词： Subgrid eddy viscosity model pressure projection method Extrapolated trape-zoidal rule The transient Navier-Stokes equations.

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Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

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Applied Mathematics and Mechanics(English Edition) 2013年第8期34卷 953-970页

作者：陈刚冯民富何银年 Department of Mathematics Sichuan University School of Mathematics and Statistics Xi'an Jiaotong University

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.

关键词： Navier-Stokes equation Ladyzhenskaya-Babu^ka-Brezzi (LBB) condition,low-order finite element pressure projection method pressure gradient local projectionmethod

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A New L^(2)projection method for the Oseen Equations

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1420-1437页

作者： Yanhong Bai Minfu Feng College of Sciences and Institute of Nonlinear DynamicsSouthwest Petroleum UniversityChengduSichuan 610500China School of Mathematics Sichuan UniversityChengduSichuan 610064China

In this paper,a new type of stabilized finite element method is discussed for Oseen equations based on the local L^(2)projection stabilized technique for the velocity *** and pressure are approximated by two kinds of mixed finite element spaces,P^(2)_( l)-P_(1),(l=1,2).A main advantage of the proposed method lies in that,all the computations are performed at the same element level,without the need of nested meshes or the projection of the gradient of velocity onto a coarse *** and convergence are proved for two kinds of stabilized *** experiments confirm the theoretical results.

关键词： Oseen equations L^(2)projection method pressure projection method

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