A posteriori error estimates for discontinuous Galerkin approximation of non-stationary convection-diffusion optimal control problems. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Zhou, Zhaojie
• Is Part Of: International journal of computer mathematics. Volume 93:Issue 12(2016)
• Page Start: 2106
• Page End: 2123
• Publication Date: 2016-12-01
• Subjects: non-stationary convection-diffusion equations -- optimal control problem -- discontinuousGalerkin method -- elliptic reconstruction -- a posteriori error estimate; 65N30; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1085031
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, we investigate a discontinuous Galerkin finite element approximation of non-stationary convection dominated diffusion optimal control problems with control constraints. The state variable is approximated by piecewise linear polynomial space and the control variable is discretized by variational discretization concept. Backward Euler method is used for time discretization. With the help of elliptic reconstruction technique residual type a posteriori error estimates are derived for state variable and adjoint state variable, which can be used to guide the mesh refinement in the adaptive algorithm. Numerical experiment is presented, which indicates the good behaviour of the a posteriori error estimators.