Optimal design problems for a non-linear cost in the gradient: numerical results

The aim of this article is the numerical study of a control problem for a linear elliptic partial differential equation. The control variable is the matrix diffusion and the functional depends non-linearly on the gradient of the state function. We consider the relaxed formulation of this problem. On...

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Bibliographic Details
Published in:Applicable analysis 2008-12, Vol.87 (12), p.1461-1487
Main Authors: Casado-Díaz, J., Couce-Calvo, J., Luna-Laynez, M., Martín-Gómez, J.D.
Format: Article
Language:English
Subjects:
composite optimal design
control in the coefficients
elliptic PDE
numerical analysis
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Summary:The aim of this article is the numerical study of a control problem for a linear elliptic partial differential equation. The control variable is the matrix diffusion and the functional depends non-linearly on the gradient of the state function. We consider the relaxed formulation of this problem. One of the main difficulties is that the functional which appears in this relaxed problem is not explicitly known. We show that in the discrete approximation, we can replace this functional by an upper or lower one.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036810802209882