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Volume 4, Issue 3-4
Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's

Konstantinos Chrysafinos

Int. J. Numer. Anal. Mod., 4 (2007), pp. 690-712.

Published online: 2007-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M60, 49M25, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-690, author = {Chrysafinos , Konstantinos}, title = {Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/884.html} }
TY - JOUR T1 - Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's AU - Chrysafinos , Konstantinos JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 690 EP - 712 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/884.html KW - error estimates, discontinuous Galerkin, optimal control, parabolic PDE's, distributed control, convection dominated, convection-diffusion equations. AB -

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.

Chrysafinos , Konstantinos. (2007). Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's. International Journal of Numerical Analysis and Modeling. 4 (3-4). 690-712. doi:
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