An Optimal EDG Method for Distributed Control of Convection Diffusion PDEs

Authors

  • Xiao Zhang
  • Yangwen Zhang Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA
  • John R. Singler Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA

Keywords:

Distributed optimal control, convection diffusion, embedded discontinuous Galerkin method, error analysis, optimize-then-discretize, discretize-then-optimize.

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 fluxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discretize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

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Published

2019-02-21

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Issue

Vol. 16 No. 4 (2019)

Section

Articles