Analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations

Authors:
Konstantinos Chrysafinos
Affiliations:
Department of Mathematics, National Technical University of Athnens, Zografou Campus, Athens 15780, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 10
Cited 1

The Velocity Tracking Problem for Navier--Stokes Flows with Bounded Distributed Controls

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Optimal Control of Distributed Systems: Theory and Applications

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Finite Element Method for Elliptic Problems
Symmetric Error Estimates for Moving Mesh Galerkin Methods for Advection-Diffusion Equations

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Analysis and Approximation of the Velocity Tracking Problem for Navier--Stokes Flows with Distributed Control

SIAM Journal on Numerical Analysis
Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations

SIAM Journal on Numerical Analysis
Perspectives in Flow Control and Optimization

Perspectives in Flow Control and Optimization
Moving Mesh Finite Element Methods for an Optimal Control Problem for the Advection-Diffusion Equation

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Error Estimates for Discontinuous Galerkin Approximations of Implicit Parabolic Equations

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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints

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LP Modelling for the Time Optimal Control Problem of the Heat Equation

Journal of Mathematical Modelling and Algorithms

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Abstract

This work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations. The minimization of the tracking functional subject to implicit parabolic equations is examined. Existence of an optimal solution is proved and an optimality system of equations is derived. Semi-discrete (in space) error estimates for the finite element approximations of the optimality system are presented. These estimates are symmetric and applicable for higher-order discretizations. Finally, fully-discrete error estimates of arbitrarily high-order are presented based on a discontinuous Galerkin (in time) and conforming (in space) scheme. Two examples related to the Lagrangian moving mesh Galerkin formulation for the convection-diffusion equation are described.