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.