W. Chen, School of Economics, Shandong University, Jinan 250100, P.R. China, e-mail: weichen@sdu.edu.cn; Q. Lin, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R. China, e-mail: linq@lsec.cc.ac.cn
Abstract: 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, numerical experiments are reported.
Keywords: eigenvalue problem, Stokes problem, stream function-vorticity-pressure method, asymptotic expansion, extrapolation, a posteriori error estimates
Classification (MSC 2000): 65N30, 65N25, 35Q30
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