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

09/01/2020
by   Alejandro Allendes, et al.
0

We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and obtain first order optimality conditions. We also obtain necessary and sufficient second order optimality conditions. To approximate the solution of the aforementioned optimal control problem we devise a finite element technique that approximates the solution to the state and adjoint equations with piecewise linear functions and the control variable with piecewise constant functions. We analyze convergence properties and prove that the error approximation of the control variable converges with rate 𝒪(h|log h|) when measured in the L^2-norm.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/14/2021

Semilinear optimal control with Dirac measures

The purpose of this work is to analyze an optimal control problem for a ...
research
12/02/2021

Optimal Control of the Kirchhoff Equation

We consider an optimal control problem for the steady-state Kirchhoff eq...
research
06/18/2022

Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs

We discretize a risk-neutral optimal control problem governed by a linea...
research
03/31/2022

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

In this paper, we carry out the numerical analysis of a non-smooth quasi...
research
06/06/2022

Energy-Time Optimal Control of Wheeled Mobile Robots

This paper focuses on the energy-time optimal control of wheeled mobile ...
research
12/17/2017

Computing Optimal Control of Cascading Failure in DC Networks

We consider discrete-time dynamics, for cascading failure in DC networks...
research
07/11/2023

Reliable optimal controls for SEIR models in epidemiology

We present and compare two different optimal control approaches applied ...

Please sign up or login with your details

Forgot password? Click here to reset