Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's

Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's

Year:    2007

Author:    Konstantinos Chrysafinos

International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 690–712

Abstract

A discontinuous Galerkin finite element method for optimal control problems having states constrained by linear parabolic PDE's is examined. The spacial operator may depend on time and need not be self-adjoint. The schemes considered here are discontinuous in time but conforming in space. Fully-discrete error estimates of arbitrary order are presented and various constants are tracked. In particular, the estimates are valid for small values of $\alpha$, $\gamma$, where $\alpha$ denotes the penalty parameter of the cost functional and $\gamma$  the coercivity constant. Finally, error estimates for the convection dominated convection-diffusion equation are presented, based on a Lagrangian moving mesh approach.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-IJNAM-884

International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 690–712

Published online:    2007-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    error estimates discontinuous Galerkin optimal control parabolic PDE's distributed control convection dominated convection-diffusion equations.

Author Details

Konstantinos Chrysafinos