Error estimates for the numerical approximation of a non-smooth quasilinear elliptic control problem

by   Christian Clason, et al.

In this paper, we carry out the numerical analysis of a non-smooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is a finitely PC^2 (continuous and C^2 apart from finitely many points) function in the state variable. Although the nonlinearity of the quasilinear elliptic equation is non-smooth, the corresponding control-to-state operator is of class C^1 but not of class C^2. Analogously, the discrete control-to-state operators associated with the approximated control problems are proven to be of class C^1 only. An explicit formula of a second-order generalized derivative of the cost functional is also established. We then exploit a second-order sufficient optimality condition to prove a priori error estimates for a variational and a piecewise constant approximation of the continuous optimal control problem.


page 1

page 2

page 3

page 4


Error estimates for a pointwise tracking optimal control problem of a semilinear elliptic equation

We consider a pointwise tracking optimal control problem for a semilinea...

Analysis and approximations of an optimal control problem for the Allen-Cahn equation

The scope of this paper is the analysis and approximation of an optimal ...

A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind

We consider an optimal control problem governed by an elliptic variation...

Error analysis for finite element approximations to the parabolic optimal control problem with measure data in a nonconvex polygon

In this paper, we establish error estimates for the numerical approximat...

A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints

We consider a one dimensional elliptic distributed optimal control probl...

Shape optimization for superconductors governed by H(curl)-elliptic variational inequalities

This paper is devoted to the theoretical and numerical study of an optim...

The fundamental solution of a 1D evolution equation with a sign changing diffusion coefficient

In this work we investigate a 1D evolution equation involving a divergen...