Volume 16, Issue 4
An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs

Xiao Zhang, Yangwen Zhang & John R. Singler

DOI:

Int. J. Numer. Anal. Mod., 16 (2019), pp. 519-542.

Published online: 2019-02

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  • Abstract

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their fluxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

  • Keywords

Distributed optimal control, convection diffusion, embedded discontinuous Galerkin method, error analysis, optimize-then-discretize, discrtize-then-optimize.

  • AMS Subject Headings

65N30, 49M25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ywzfg4@mst.edu (Yangwen Zhang)

singlerj@mst.edu (John R. Singler)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-519, author = {Xiao Zhang , and Zhang , Yangwen and Singler , John R. }, title = {An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {4}, pages = {519--542}, abstract = {

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their fluxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13013.html} }
TY - JOUR T1 - An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs AU - Xiao Zhang , AU - Zhang , Yangwen AU - Singler , John R. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 519 EP - 542 PY - 2019 DA - 2019/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13013.html KW - Distributed optimal control, convection diffusion, embedded discontinuous Galerkin method, error analysis, optimize-then-discretize, discrtize-then-optimize. AB -

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their fluxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Xiao Zhang, Yangwen Zhang & John R. Singler. (2019). An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs. International Journal of Numerical Analysis and Modeling. 16 (4). 519-542. doi:
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