Open Access Research

Adaptive fully-discrete finite element methods for nonlinear quadratic parabolic boundary optimal control

Zuliang Lu

Author Affiliations

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:10.1186/1687-2770-2013-72

Published: 4 April 2013

Abstract

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.