Optimal design problems for a non-linear cost in the gradient: numerical results
Juan Casado‐Díaz, Julio Couce-Calvo, Manuel Luna‐Laynez, José D. Martín-Gómez · Applicable Analysis · 2008
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.