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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

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.

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

Wei Chen, Qun Lin (2006)

Applications of Mathematics

By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...

Asymmetric heteroclinic double layers

Michelle Schatzman (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Let W be a non-negative function of class C 3 from 2 to , which vanishes exactly at two points 𝐚 and 𝐛 . Let S 1 ( 𝐚 , 𝐛 ) be the set of functions of a real variable which tend to 𝐚 at - and to 𝐛 at + and whose one dimensional energy E 1 ( v ) = W ( v ) + | v ' | 2 / 2 d x is finite. Assume that there exist two isolated minimizers z + and z - of the energy E 1 over S 1 ( 𝐚 , 𝐛 ) . Under a mild coercivity condition on the potential W and a generic spectral condition on the linearization of the one-dimensional Euler–Lagrange operator at z + and z - , it is possible to prove...

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