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.
Highlights
1 Introduction In this paper, we study the fully-discrete finite element approximation for quadratic boundary optimal control problems governed by nonlinear parabolic equations
The finite element approximation of a linear elliptic optimal control problem is well investigated by Falk [ ] and Geveci [ ]
The discretization for semilinear elliptic optimal control problems is discussed by Arada, Casas, and Tröltzsch in [ ]
Summary
1 Introduction In this paper, we study the fully-discrete finite element approximation for quadratic boundary optimal control problems governed by nonlinear parabolic equations. Finite element approximation of optimal control problems plays a very important role in the numerical methods for these problems. The finite element approximation of a linear elliptic optimal control problem is well investigated by Falk [ ] and Geveci [ ]. Systematic introductions of the finite element method for optimal control problems can be found in [ – ].
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