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Volume 29, Issue 1
Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints

Klaus Deckelnick & Michael Hinze

DOI: 10.4208/jcm.1006-m3213

J. Comp. Math., 29 (2011), pp. 1-15.

Published online: 2011-02

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  • Abstract

We consider a parabolic optimal control problem with pointwise state constraints. The optimization problem is approximated by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. Error bounds for control and state are obtained both in two and three space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements.

  • Keywords

Parabolic optimal control problem, State constraints, Error estimates.

  • AMS Subject Headings

49J20, 49K20, 35B37.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-1, author = {Klaus Deckelnick and Michael Hinze}, title = {Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {1}, pages = {1--15}, abstract = {

We consider a parabolic optimal control problem with pointwise state constraints. The optimization problem is approximated by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. Error bounds for control and state are obtained both in two and three space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1006-m3213}, url = {http://global-sci.org/intro/article_detail/jcm/8460.html} }
TY - JOUR T1 - Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints AU - Klaus Deckelnick & Michael Hinze JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 15 PY - 2011 DA - 2011/02 SN - 29 DO - http://doi.org/10.4208/jcm.1006-m3213 UR - https://global-sci.org/intro/article_detail/jcm/8460.html KW - Parabolic optimal control problem, State constraints, Error estimates. AB -

We consider a parabolic optimal control problem with pointwise state constraints. The optimization problem is approximated by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. Error bounds for control and state are obtained both in two and three space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements.

Klaus Deckelnick and Michael Hinze. (2011). Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints. Journal of Computational Mathematics. 29 (1). 1-15. doi:10.4208/jcm.1006-m3213
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