A Time Discretization Scheme for a Non local Degenerate Problem Modelling Resistance Spot Welding

作者：Kavallaris N I^*; Yan Y

来源：Mathematical Modelling of Natural Phenomena, 2015, 10(6): 90-112.

DOI：10.1051/mmnp/201510608

• Non-local
• degenerate parabolic equation
• moving boundary
• stability
• error estimates
• Chernoff formula
• resistance spot welding

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.

• 出版日期2015