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A mixed formulation for the direct approximation of L2-weighted controls for the linear heat equation

Opened Access A mixed formulation for the direct approximation of L2-weighted controls for the linear heat equation

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Autor: Münch, Arnaud
Araujo de Souza, Diego
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2016-02
Publicado en: Advances in Computational Mathematics, 42 (1), 85-125.
Tipo de documento: Artículo
Resumen: This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a given positive time. In [Fernandez-Cara & Münch, Strong convergence approximations of null controls for the 1D heat equation, 2013], a so-called primal method is described leading to a strongly convergent approximation of distributed control: the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality conditions. In this work, we adapt the method to approximate the control of minimal square integrable-weighted norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and its adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach c...
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Cita: Münch, A. y Araujo de Souza, D. (2016). A mixed formulation for the direct approximation of L2-weighted controls for the linear heat equation. Advances in Computational Mathematics, 42 (1), 85-125.
Tamaño: 1.247Mb
Formato: PDF

URI: http://hdl.handle.net/11441/47659

DOI: 10.1007/s10444-015-9412-5

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