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Approximation and numerical realization of an optimal design welding problem
Author(s) -
Chakib A.,
Nachaoui A.,
Nachaoui M.
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21767
Subject(s) - discretization , realization (probability) , mathematics , convergence (economics) , sequence (biology) , partial differential equation , mathematical optimization , boundary (topology) , process (computing) , boundary value problem , mathematical analysis , computer science , statistics , biology , economics , genetics , economic growth , operating system
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