New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

• Main Authors: Zuliang Lu, Hongyan Liu, Chunjuan Hou, Longzhou Cao
• Format: Article
• Language: English
• Published: SpringerOpen 2016-02-01
• Series: Journal of Inequalities and Applications
• Subjects: residual-based a posteriori error estimates; nonlinear parabolic optimal control problems; hp version of finite element method
• Online Access: http://link.springer.com/article/10.1186/s13660-016-0994-3
• ISSN: 1029-242X

Abstract In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems.