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Volume 36, Issue 5
A Full Discrete Stabilized Method for the Optimal Control of the Unsteady Navier-Stokes Equations

Yanmei Qin, Gang Chen & Minfu Feng

DOI: 10.4208/jcm.1703-m2016-0693

J. Comp. Math., 36 (2018), pp. 718-738.

Published online: 2018-06

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  • Abstract

In this paper, a full discrete local projection stabilized (LPS) method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficiently smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.

  • Keywords

Optimal control, Unsteady Navier-Stokes equations, High Reynolds number, Full discrete, Local projection stabilization.

  • AMS Subject Headings

49J20, 49K20, 65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

qinyanmei0809@163.com (Yanmei Qin)

569615491@qq.com (Gang Chen)

fmf@wtjs.cn (Minfu Feng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-718, author = {Qin , YanmeiChen , Gang and Feng , Minfu}, title = {A Full Discrete Stabilized Method for the Optimal Control of the Unsteady Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {5}, pages = {718--738}, abstract = {

In this paper, a full discrete local projection stabilized (LPS) method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficiently smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1703-m2016-0693}, url = {http://global-sci.org/intro/article_detail/jcm/12454.html} }
TY - JOUR T1 - A Full Discrete Stabilized Method for the Optimal Control of the Unsteady Navier-Stokes Equations AU - Qin , Yanmei AU - Chen , Gang AU - Feng , Minfu JO - Journal of Computational Mathematics VL - 5 SP - 718 EP - 738 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1703-m2016-0693 UR - https://global-sci.org/intro/article_detail/jcm/12454.html KW - Optimal control, Unsteady Navier-Stokes equations, High Reynolds number, Full discrete, Local projection stabilization. AB -

In this paper, a full discrete local projection stabilized (LPS) method is proposed to solve the optimal control problems of the unsteady Navier-Stokes equations with equal order elements. Convective effects and pressure are both stabilized by using the LPS method. A priori error estimates uniformly with respect to the Reynolds number are obtained, providing the true solutions are sufficiently smooth. Numerical experiments are implemented to illustrate and confirm our theoretical analysis.

Qin , YanmeiChen , Gang and Feng , Minfu. (2018). A Full Discrete Stabilized Method for the Optimal Control of the Unsteady Navier-Stokes Equations. Journal of Computational Mathematics. 36 (5). 718-738. doi:10.4208/jcm.1703-m2016-0693
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