Optimal control of the convection-diffusion equation using stabilized finite element methods

Authors:
Roland Becker;Boris Vexler
Affiliations:
Université de Pau et des Pays de l’Adour, Laboratoire de Mathématiques Appliquées, BP 1155, 64013, PAU Cedex, France;Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics (RICAM), BP 1155, Altenberger Straße 69, 4040, Linz, Austria
Venue:
Numerische Mathematik
Year:
2007

Citing 0
Cited 17

A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equation

Journal of Computational and Applied Mathematics
A priori error estimates for elliptic optimal control problems with a bilinear state equation

Journal of Computational and Applied Mathematics
A RT Mixed FEM/DG Scheme for Optimal Control Governed by Convection Diffusion Equations

Journal of Scientific Computing
A characteristic finite element method for optimal control problems governed by convection-diffusion equations

Journal of Computational and Applied Mathematics
Numerical approximation of the LQR problem in a strongly damped wave equation

Computational Optimization and Applications
Error analysis for optimal control problem governed by convection diffusion equations: DG method

Journal of Computational and Applied Mathematics
Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems

SIAM Journal on Numerical Analysis
A Generalization of the Local Projection Stabilization for Convection-Diffusion-Reaction Equations

SIAM Journal on Numerical Analysis
A Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem

SIAM Journal on Scientific Computing
A Priori Error Analysis of the Petrov-Galerkin Crank-Nicolson Scheme for Parabolic Optimal Control Problems

SIAM Journal on Control and Optimization
Original article: Characteristic mixed finite element approximation of transient convection diffusion optimal control problems

Mathematics and Computers in Simulation
Investigation of Commutative Properties of Discontinuous Galerkin Methods in PDE Constrained Optimal Control Problems

Journal of Scientific Computing
Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method

Journal of Computational and Applied Mathematics
An optimization-based approach to enforcing mass conservation in level set methods

Journal of Computational and Applied Mathematics
Third order convergent time discretization for parabolic optimal control problems with control constraints

Computational Optimization and Applications
Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization

Journal of Computational and Applied Mathematics
A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations

Computational Optimization and Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then- discretize” and “discretize-then-optimize” coincide for the proposed discretization scheme. This allows for a symmetric optimality system at the discrete level and optimal order of convergence.