Optimización dispersa de ecuaciones diferenciales parciales elípticas en un espacio de control finito con restricciones de control y estado

Abstract

The purpose of this study is deriving an estimation of the generated error due to the numerical approximation of a optimal control problem governed by linear elliptic partial differential equations with homogeneous Dirichlet boundary conditions (by the finite element method) with the following particularities: i) The control space is finite dimentional. ii) Pointwise state constraints are imposed in the domain of equation. iii) The functional cost includes a norm 1 penalization, which is non-differentiable. It is proved that the order of convergence for the error is h^2|log h|, where h represents the size of the mesh. Finally, to illustrate this estimation, numerical experiments are conducted.