Approximation of an Eigenvalue Problem Associated with the Stokes Problem by the Stream Function-Vorticity-Pressure Method |
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Authors: | Wei Chen Qun Lin |
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Institution: | (1) School of Economics, Shandong University, Jinan, 250100, P.R. China;(2) Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, P.R. China |
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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.
The first author was supported by China Postdoctoral Sciences Foundation. |
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Keywords: | eigenvalue problem Stokes problem stream function-vorticity-pressure method asymptotic expansion extrapolation a posteriori error estimates |
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