Approximation of Sparse Controls in Semilinear Elliptic Equations

Approximation of sparse controls in semilinear equations by piecewise linear functions

Abstract. Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, ...

A Posteriori Error Estimates for Semilinear Boundary Control Problems

In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...

Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R. Piecewise linear finite elements are used to approximate the control as well as the state...