Error analysis of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation. Issue 5 (23rd March 2017)

• Record Type: Journal Article
• Authors: Liu, Huipo; Wang, Shuanghu; Han, Hongbin; Yuan, Lan
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 5(2017:Sep.)
• Page Start: 1493
• Page End: 1512
• Publication Date: 2017-03-23
• Subjects: a posteriori error estimate -- a priori error estimate -- discontinuous Galerkin finite element method -- optimal control -- transport equation; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22149
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : This article discusses a priori and a posteriori error estimates of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation. We use variational discretization concept to discretize the control variable and discontinuous piecewise linear finite elements to approximate the state and costate variable. Based on the error estimates of discontinuous Galerkin finite element method for the transport equation, we get a priori and a posteriori error estimates for the transport equation optimal control problem. Finally, two numerical experiments are carried out to confirm the theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1493–1512, 2017