An HDG Method for Distributed Control of Convection Diffusion PDEs
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 L2 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 L2 norm. We present 2D and 3D numerical experiments to illustrate our theoretical results.
G. Chen et al., "An HDG Method for Distributed Control of Convection Diffusion PDEs," Journal of Computational and Applied Mathematics, vol. 343, pp. 643-661, Elsevier B.V., Dec 2018.
The definitive version is available at https://doi.org/10.1016/j.cam.2018.05.028
Mathematics and Statistics
Keywords and Phrases
Distributed optimal control; Error analysis; Hybridizable discontinuous Galerkin method; Linear convection diffusion equation; Postprocessing; Superconvergence
International Standard Serial Number (ISSN)
Article - Journal
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