Approximation and numerical realization of an optimal design welding problem

In this article, we deal with the approximation of an optimal shape design approach for a free boundary problem modeling a welding process. We consider discretization of this problem based on linear finite elements. We prove the existence of discrete optimal solutions. This allows us to show the con...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2013-09, Vol.29 (5), p.1563-1586
Main Authors: Chakib, A., Nachaoui, A., Nachaoui, M.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Discretization
finite element
Free boundaries
free boundary
Mathematical analysis
Mathematical models
noncoercive operator
Optimization
shape optimization
Welding
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Summary:In this article, we deal with the approximation of an optimal shape design approach for a free boundary problem modeling a welding process. We consider discretization of this problem based on linear finite elements. We prove the existence of discrete optimal solutions. This allows us to show the convergence result of a sequence of discrete solutions to the continuous one. Finally, methods for numerical realization are described and several examples have been carried out to illustrate the efficiency of the proposed approach. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21767