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An HDG method for distributed control of convection diffusion PDEs.
- Source :
-
Journal of Computational & Applied Mathematics . Dec2018, Vol. 343, p643-661. 19p. - Publication Year :
- 2018
-
Abstract
- We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic linear convection diffusion PDE. We use degree k polynomials to approximate the state, adjoint state, their fluxes, and the optimal control, and we show the approximations converge with order k + 1 in the L 2 norm. Finally, we use a simple element-by-element postprocessing scheme to obtain new superconvergent approximations of the state, dual state and the control. We show the postprocessed variables converge with order k + 2 in the L 2 norm. We present 2D and 3D numerical experiments to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 343
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 130223404
- Full Text :
- https://doi.org/10.1016/j.cam.2018.05.028