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Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations

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In this paper we focus on numerical analysis of finite element methods with stabilizations for the optimal control of system governed by unsteady Oseen equations. Using continuous equal-order finite elements for both velocities and pressure, two fully discrete schemes are proposed. Convective effects and pressure are stabilized by adding a subgrid scale eddy viscosity term and a pressure stabilized term. Convergence of the approximate solution is proved. A-Priori error estimates are obtained uniformly with Reynolds number, especially the \(L^2\)-error estimates of numerical solution are independent of Reynolds number. The numerical experiments are shown to be consistent with our theoretical analysis.

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Acknowledgments

This research is supported by the Natural Science Foundation of China (No. 11271273). The authors would like to thank the editors and referees for their criticism, valuable comments and suggestions which helped to improve this paper. The authors also would like to thank Huanchen Bao, Shuo Zhou, Weidong Wang and Qiao He for their checking of this paper.

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  1. School of Mathematics, Sichuan University, Chengdu , 610064, China

    Gang Chen & Minfu Feng

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  1. Gang Chen
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  2. Minfu Feng
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Correspondence to Minfu Feng.

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Chen, G., Feng, M. Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations. Comput Optim Appl 58, 679–705 (2014). https://doi.org/10.1007/s10589-014-9649-9

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  • DOI: https://doi.org/10.1007/s10589-014-9649-9

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