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Solving ill-posed c...
Solving ill-posed control problems by stabilized finite element methods : an alternative to Tikhonov regularization
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- Burman, Erik (författare)
- University College London, London, UK
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- Hansbo, Peter (författare)
- Jönköping University,JTH, Material och tillverkning
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- Larson, Mats G. (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå University, Umeå, Sweden
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(creator_code:org_t)
- 2018-01-31
- 2018
- Engelska.
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Ingår i: Inverse Problems. - : IOP PUBLISHING LTD. - 0266-5611 .- 1361-6420. ; 34:3
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Abstract
Ämnesord
Stäng
- Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely illposed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson's equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- optimal control problem
- data assimilation
- source identification
- finite elements
- regularization
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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