Numerical Analysis of a System of Singularly Perturbed Convection-Diffusion Equations Related to Optimal Control
Hans-Gorg Roos 1, Christian Reibiger 1*1 Technische Universitat Dresden, Institut fur Numerische Mathematik, 01062 Dresden, Germany.
Received 15 January 2011; Accepted (in revised version) 16 March 2011
We consider an optimal control problem with an 1D singularly perturbed differential state equation. For solving such problems one uses the enhanced system of the state equation and its adjoint form. Thus, we obtain a system of two convection-diffusion equations. Using linear finite elements on adapted grids we treat the effects of two layers arising at different boundaries of the domain. We proof uniform error estimates for this method on meshes of Shishkin type. We present numerical results supporting our analysis.AMS subject classifications: 34E05, 34E20, 65L10, 65L11, 65L60, 65L70
Key words: Convection-diffusion, linear finite elements, a priori analysis, layer-adapted meshes, singular perturbed, optimal control.
Email: Hans-Goerg.Roos@tu-dresden.de (H.-G. Roos), Christian.Reibiger@tu-dresden.de (C. Reibiger)