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An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
Published online by Cambridge University Press: 28 June 2011
Abstract
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin method. A priori error estimates are developed at different discretization levels. Numerical experiments presented justify the theoretical order of convergence obtained.
Keywords
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 6 , November 2011 , pp. 1081 - 1113
- Copyright
- © EDP Sciences, SMAI, 2011
References
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