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PENALTY-FACTOR-FREE STABILIZED nonconforming finite elements FOR SOLVING STATIONARY NAVIER-STOKES EQUATIONS

Journal of Computational Mathematics 2022年第5期40卷 728-755页

作者： Linshuang He Minfu Feng Qiang Ma School of Mathematics Sichuan UniversityChengdu 610064China

Two nonconforming penalty methods for the two-dimensional stationary Navier-Stokes equations are studied in this *** methods are based on the weakly continuous P1 vector fields and the locally divergence-free(LDF)finite elements,which respectively penalize local divergence and are discontinuous across *** methods have no penalty factors and avoid solving the saddle-point *** existence and uniqueness of the velocity solution are proved,and the optimal error estimates of the energy norms and L^(2)-norms are ***,we propose unified pressure recovery algorithms and prove the optimal error estimates of L^(2)-norm for *** design a unified iterative method for numerical experiments to verify the correctness of the theoretical analysis.

关键词： Stationary Navier-Stokes equations nonconforming finite elements Penalty stabilization methods DG methods Locally divergence-free.

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On the error bounds of nonconforming finite elements

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Science China Mathematics 2010年第11期53卷 2917-2926页

作者： MAO ShiPeng SHI ZhongCi The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.

关键词： nonconforming finite elements Cea’s lemma error estimates

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TWO-GRID DISCRETIZATION SCHEMES OF THE nonconforming FEM FOR EIGENVALUE PROBLEMS

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Journal of Computational Mathematics 2009年第6期27卷 748-763页

作者： Yidu Yang School of Mathematics and Computer Science Guizhou Normal University Guiyang 550001 China

This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou （Math. Comput., 70 （2001）, pp.17-25） to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly.

关键词： nonconforming finite elements Rayleigh quotient Two-grid schemes The lower bounds of eigenvalue High accuracy.

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A Family of nonconforming Rectangular elements for Strain Gradient Elasticity

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Advances in Applied Mathematics and Mechanics 2019年第6期11卷 1263-1286页

作者： Yulei Liao Pingbing Ming School of Mathematics Renmin University of ChinaNo.59Zhongguancun StreetBeijing 100872China LSEC Institute of Computational MathematicsAMSS Chinese Academy of SciencesNo.55East Road ZhongguancunBeijing 100190Chinaand School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China

We propose a family of nonconforming rectangular elements for the linear strain gradient elastic *** error estimates uniformly with respect to the small material parameter have been *** results confirm the theoretical... 详细信息

关键词： nonconforming finite elements strain gradient elasticity uniform error estimate

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