Volume 1, Issue 3
A Priori and a Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

Ningning Yan & Zhaojie Zhou

Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 297-320.

Published online: 2008-01

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  • Abstract

In this paper, we investigate a streamline diffusion finite element approximation scheme for the constrained optimal control problem governed by linear convection dominated diffusion equations. We prove the existence and uniqueness of the discretized scheme. Then a priori and a posteriori error estimates are derived for the state, the co-state and the control. Three numerical examples are presented to illustrate our theoretical results.

  • Keywords

Constrained optimal control problem, convection dominated diffusion equation, streamline diffusion finite element method, a priori error estimate, a posteriori error estimate.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-297, author = {}, title = {A Priori and a Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {3}, pages = {297--320}, abstract = {

In this paper, we investigate a streamline diffusion finite element approximation scheme for the constrained optimal control problem governed by linear convection dominated diffusion equations. We prove the existence and uniqueness of the discretized scheme. Then a priori and a posteriori error estimates are derived for the state, the co-state and the control. Three numerical examples are presented to illustrate our theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6053.html} }
TY - JOUR T1 - A Priori and a Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 297 EP - 320 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6053.html KW - Constrained optimal control problem, convection dominated diffusion equation, streamline diffusion finite element method, a priori error estimate, a posteriori error estimate. AB -

In this paper, we investigate a streamline diffusion finite element approximation scheme for the constrained optimal control problem governed by linear convection dominated diffusion equations. We prove the existence and uniqueness of the discretized scheme. Then a priori and a posteriori error estimates are derived for the state, the co-state and the control. Three numerical examples are presented to illustrate our theoretical results.

Ningning Yan & Zhaojie Zhou. (2020). A Priori and a Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation. Numerical Mathematics: Theory, Methods and Applications. 1 (3). 297-320. doi:
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