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

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.

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

Document Type: Research article

DOI: 10.1080/00036810802209882

Affiliations: 1: Facultad de Matematicas, Departmento de Ecuaciones Diferenciales y Analisis Numerico, University of Seville, Sevilla, Spain