Adaptive fully-discrete finite element methods for nonlinear quadratic parabolic boundary optimal control
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, P.R. China
College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, P.R. China
Boundary Value Problems 2013, 2013:72 doi:10.1186/1687-2770-2013-72Published: 4 April 2013
The aim of this work is to study adaptive fully-discrete finite element methods for quadratic boundary optimal control problems governed by nonlinear parabolic equations. We derive a posteriori error estimates for the state and control approximation. Such estimates can be used to construct reliable adaptive finite element approximation for nonlinear quadratic parabolic boundary optimal control problems. Finally, we present a numerical example to show the theoretical results.