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Numerical Analysis of a System of Singularly Perturbed Convection-Diffusion Equations Related to Optimal Control

Published online by Cambridge University Press:  28 May 2015

Hans-Görg Roos  and
Christian Reibiger
Hans-Görg Roos*
Affiliation:
Technische Universität Dresden, Institut für Numerische Mathematik, 01062 Dresden, Germany
Christian Reibiger*
Affiliation:
Technische Universität Dresden, Institut für Numerische Mathematik, 01062 Dresden, Germany
*
Corresponding author.Email address:Hans-Goerg.Roos@tu-dresden.de
Corresponding author.Email address:Christian.Reibiger@tu-dresden.de
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Abstract

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.

Keywords

34E0534E2065L1065L1165L6065L70Convection-diffusionlinear finite elementsa priori analysislayer-adapted meshessingular perturbedoptimal control
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 562 - 575
Copyright
Copyright © Global Science Press Limited 2011

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