Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method

Wei Chen; Qun Lin

Displaying similar documents to “Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method”

Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods

Shanghui Jia, Hehu Xie, Xiaobo Yin, Shaoqin Gao (2009)

Applications of Mathematics

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In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, $Q_{1}^{rot}$ and $E Q_{1}^{rot}$ . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations. ...

Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems

Hongtao Chen, Shanghui Jia, Hehu Xie (2009)

Applications of Mathematics

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In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space.

Mixed approximation of eigenvalue problems: A superconvergence result

Francesca Gardini (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini...

Finite element approximation of a contact vector eigenvalue problem

Hennie de Schepper, Roger Van Keer (2003)

Applications of Mathematics

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We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem....

Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

Qin Li, Qun Lin, Hehu Xie (2013)

Applications of Mathematics

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The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, $Q_{1}^{rot}$ , $E Q_{1}^{rot}$ and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented...