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AN hp-DISCONTINUOUS GALERKIN METHOD FOR THE OPTIMAL CONTROL PROBLEM OF LASER SURFACE HARDENING OF STEEL

DSpace at IIT Bombay

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Title AN hp-DISCONTINUOUS GALERKIN METHOD FOR THE OPTIMAL CONTROL PROBLEM OF LASER SURFACE HARDENING OF STEEL
 
Creator NUPUR, G
NEELA, N
 
Subject FINITE-ELEMENT METHODS
BOUNDARY-VALUE-PROBLEMS
PARABOLIC PROBLEMS
PHASE-TRANSITIONS
ELLIPTIC PROBLEMS
NONMONOTONE TYPE
MODEL
PENALTY
Laser surface hardening of steel
semi-linear parabolic equation
optimal control
error estimates
discontinuous Galerkin finite element method
 
Description 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.
 
Publisher CAMBRIDGE UNIV PRESS
 
Date 2012-06-26T09:37:21Z
2012-06-26T09:37:21Z
2011
 
Type Article
 
Identifier ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,45(6)1081-1113
0764-583X
http://dx.doi.org/10.1051/m2an/2011013
http://dspace.library.iitb.ac.in/jspui/handle/100/14305
 
Language English