Optimal control of the convection-diffusion equation using stabilized finite element methods

被引：1
作者：
Roland Becker
Boris Vexler
机构：
[1] Université de Pau et des Pays de l’Adour,Laboratoire de Mathématiques Appliquées
[2] Austrian Academy of Sciences,Johann Radon Institute for Computational and Applied Mathematics (RICAM)
来源：
Numerische Mathematik | 2007年 / 106卷
关键词：
Optimal control; Stabilized finite elements; Error estimates; Pointwise inequality constraints;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then- discretize” and “discretize-then-optimize” coincide for the proposed discretization scheme. This allows for a symmetric optimality system at the discrete level and optimal order of convergence.
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页码：349 / 367
页数：18
相关论文
共 25 条
[1]  
Arada N.(2002)Error estimates for a semilinear elliptic optimal control problem Comput. Optim. Approx. 23 201-229
[2]  
Casas E.(2001)A finite element pressure gradient stabilization for the stokes equations based on local projections Calcolo 38 137-199
[3]  
Tröltzsch F.(1999)Primal-dual strategy for constrained optimal control problems SIAM J. Control Optim. 37 1176-1194
[4]  
Becker R.(2006)Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method SIAM J. Numer. Anal. 43 2544-2566
[5]  
Braack M.(2004)Edge stabilization for Galerkin approximations of convection–diffusion–reaction problems Comput. Methods Appl. Mech. Eng. 193 1437-1453
[6]  
Bergounioux M.(2005)Optimal control and numerical adaptivity for advection-diffusion equations M2AN 39 1019-1040
[7]  
Ito K.(1973)Approximation of a class of optimal control problems with order of convergence estimates J. Math. Anal. Appl. 44 28-47
[8]  
Kunisch K.(1999)Stabilization of Galerkin approximations of transport equations by subgrid modeling Modél. Math. Anal. Numér. 36 1293-1316
[9]  
Braack M.(2005)A variational discretization concept in control constrained optimization: the linear-quadratic case Comput. Optim. Appl. 30 45-61
[10]  
Burman E.(2002)Primal-dual active set strategy for a general class of constrained optimal control problems SIAM J. Optim. 13 321-334
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