Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations

被引：37

作者：

Negri, Federico ^{[1
]}

Manzoni, Andrea ^{[1
]}

Rozza, Gianluigi ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, CMCS MATHICSE SB, CH-1015 Lausanne, Switzerland

[2] SISSA Mathlab, Int Sch Adv Studies, I-34136 Trieste, Italy

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2015年 / 69卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Reduced basis method; Optimal flow control; Saddle-point problems; PDE-constrained optimization; A posteriori error estimates; FINITE-ELEMENT APPROXIMATION; POSTERIORI ERROR ESTIMATION; STABILITY;

D O I：

10.1016/j.camwa.2014.12.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates - and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：319 / 336

页数：18

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