An HDG Method for Distributed Control of Convection Diffusion PDEs

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.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Distributed optimal control; Error analysis; Hybridizable discontinuous Galerkin method; Linear convection diffusion equation; Postprocessing; Superconvergence

International Standard Serial Number (ISSN)

0377-0427

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Elsevier B.V., All rights reserved.

Publication Date

01 Dec 2018

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