Hinze, Michael; Slawig, Thomas Adjoint gradients compared to gradients from algorithmic differentiation in instantaneous control of the Navier–Stokes equations. (English) Zbl 1051.49017 Optim. Methods Softw. 18, No. 3, 299-315 (2003). Summary: Gradients computed via an adjoint equation and obtained algorithmically by automatic differentiation (AD) tools are compared with respect to accuracy and performance. As model application, the method of instantaneous control for the time-dependent incompressible Navier-Stokes equations with distributed control is used. The method of instantaneous control and both approaches to obtain the gradient are described in detail. Implementation issues of the AD process are given. Numerical results for gradient evaluations and complete control runs on different grids are presented. Cited in 2 Documents MSC: 49M25 Discrete approximations in optimal control 49J20 Existence theories for optimal control problems involving partial differential equations 76D05 Navier-Stokes equations for incompressible viscous fluids 65K10 Numerical optimization and variational techniques 76D55 Flow control and optimization for incompressible viscous fluids Keywords:instantaneous control; adjoint equation; algorithmic differentiation; Navier-Stokes equations; accuracy; performance; adjoint gradients; discretization Software:TAF; TAMC PDFBibTeX XMLCite \textit{M. Hinze} and \textit{T. Slawig}, Optim. Methods Softw. 18, No. 3, 299--315 (2003; Zbl 1051.49017) Full Text: DOI