Article
An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs
International Journal of Numerical Analysis and Modeling
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 uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.
Department(s)
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
- Convection diffusion,
- Discrtize-then-optimize,
- Distributed optimal control,
- Embedded discontinuous galerkin method,
- Error analysis,
- Optimize-then-discretize
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Publication Date
10-1-2019
Publication Date
01 Oct 2019
Disciplines
Citation Information
X. Zhang, Y. Zhang and John R. Singler. "An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs" International Journal of Numerical Analysis and Modeling Vol. 16 Iss. 4 (2019) p. 519 - 542 ISSN: 1705-5105 Available at: http://works.bepress.com/john-singler/56/
X. Zhang thanks Missouri University of Science and Technology for hosting him as a visiting scholar; some of this work was completed during his research visit. Y. Zhang and J. Singler were supported in part by National Science Foundation grant DMS-1217122. Y. Zhang and J. Singler thank the IMA for funding research visits, during which some of this work was completed.