Geodesic
A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding
N. I. Kavallaris1 ; Y. Yan1
1 Department of Mathematics, University of Chester Thornton Science Park Pool Lane, Ince, Chester CH2 4NU, UK
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 6, pp. 90-112

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In the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a correction to account for the nonlinearity. The stability and error estimates of the developed scheme are investigated. Finally some numerical results are presented confirming the efficiency of the developed numerical algorithm.
DOI : 10.1051/mmnp/201510608

N. I. Kavallaris 1 ; Y. Yan 1

1 Department of Mathematics, University of Chester Thornton Science Park Pool Lane, Ince, Chester CH2 4NU, UK 
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N. I. Kavallaris; Y. Yan. A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 6, pp. 90-112. doi: 10.1051/mmnp/201510608

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