Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901860 | Journal of Computational and Applied Mathematics | 2018 | 19 Pages |
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 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Gang Chen, Weiwei Hu, Jiguang Shen, John R. Singler, Yangwen Zhang, Xiaobo Zheng,