On numerical approximation of an optimal control problem in linear elasticity

• Autor(a) principal: Rincon, Mauro Antônio
• Data de Publicação: 1999
• Outros Autores: Liu, I-Shih
• Tipo de documento: Relatório
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRJ
• Texto Completo: http://hdl.handle.net/11422/2663
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO::MODELOS ANALITICOS E DE SIMULACAO; Elasticidade linear; Método dos elementos finitos; Iterative method; Linear elasticity; Finite element method; Optimal control

In this paper we apply the optimal control theory to a linear elasticity problem. An iterative method based on the optimality system characterizing the corresponding minimization of a cost functional is proposed. Convergence of the approximate solutions is proved provided that a parameter of penalization is not too small. Numerical solutions are presented to emphasize the role of this parameter. It is shown that the results are far from being good approximations of the expected ones, because the parameter can not be taken small enough in the iteration method. On the other hand, numerical results from a spectral analysis are shown without this limitation by the use of eigenfunction representations.