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

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. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applicable Analysis: An International Journal Taylor & Francis

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

27 pages

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References (35)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1563-504X
eISSN
0003-6811
DOI
10.1080/00036810802209882
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Applicable Analysis: An International JournalTaylor & Francis

Published: Dec 1, 2008

Keywords: control in the coefficients; elliptic PDE; composite optimal design; numerical analysis; 49M25; 49J20

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