Two-level stabilized finite element method for Stokes eigenvalue problem |
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Authors: | Peng-zhan Huang Yin-nian He Xin-long Feng |
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Affiliation: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China;2. Center for Computational Geoscienes, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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Abstract: | A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h = O(H 2), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method. |
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Keywords: | Stokes eigenvalue problem stabilized method lowest equal-order pair two-level method |
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