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Volume 20, Issue 3
Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics

Pelin G. Geredeli, Carson Givens & Ahmed Zytoon

DOI: 10.4208/ijnam2023-1013

Int. J. Numer. Anal. Mod., 20 (2023), pp. 329-352.

Published online: 2023-03

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  • Abstract

In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite element method (FEM) and finite difference method (FDM) approximations to show that the null controllers being approximated via FEM and FDM exhibit exactly the same asymptotics of the associated minimal energy function. For this, we appeal to the theory originally given by R. Triggiani [20] for construction of null controllers of ODE systems. These null controllers are also amenable to our numerical implementation in which we discuss the aspects of FEM and FDM numerical approximations and compare both methodologies. We justify our theoretical results with the numerical experiments given for both approximation schemes.

code-IJNAM-2023-03-02(Null-control).zip

  • Keywords

Null control, finite element method, finite difference method.

  • AMS Subject Headings

65M60, 65N06, 35A15

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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  • TXT
@Article{IJNAM-20-329, author = {Geredeli , Pelin G.Givens , Carson and Zytoon , Ahmed}, title = {Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {3}, pages = {329--352}, abstract = {

In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite element method (FEM) and finite difference method (FDM) approximations to show that the null controllers being approximated via FEM and FDM exhibit exactly the same asymptotics of the associated minimal energy function. For this, we appeal to the theory originally given by R. Triggiani [20] for construction of null controllers of ODE systems. These null controllers are also amenable to our numerical implementation in which we discuss the aspects of FEM and FDM numerical approximations and compare both methodologies. We justify our theoretical results with the numerical experiments given for both approximation schemes.

code-IJNAM-2023-03-02(Null-control).zip

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1013}, url = {http://global-sci.org/intro/article_detail/ijnam/21536.html} }
TY - JOUR T1 - Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics AU - Geredeli , Pelin G. AU - Givens , Carson AU - Zytoon , Ahmed JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 329 EP - 352 PY - 2023 DA - 2023/03 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1013 UR - https://global-sci.org/intro/article_detail/ijnam/21536.html KW - Null control, finite element method, finite difference method. AB -

In this paper, we consider a structurally damped elastic equation under hinged boundary conditions. Fully-discrete numerical approximation schemes are generated for the null controllability of these parabolic-like PDEs. We mainly use finite element method (FEM) and finite difference method (FDM) approximations to show that the null controllers being approximated via FEM and FDM exhibit exactly the same asymptotics of the associated minimal energy function. For this, we appeal to the theory originally given by R. Triggiani [20] for construction of null controllers of ODE systems. These null controllers are also amenable to our numerical implementation in which we discuss the aspects of FEM and FDM numerical approximations and compare both methodologies. We justify our theoretical results with the numerical experiments given for both approximation schemes.

code-IJNAM-2023-03-02(Null-control).zip

Pelin G. Geredeli, Carson Givens & Ahmed Zytoon. (2023). Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics. International Journal of Numerical Analysis and Modeling. 20 (3). 329-352. doi:10.4208/ijnam2023-1013
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