| Issue |
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
|
|
|---|---|---|
| Page(s) | 90 - 112 | |
| DOI | https://doi.org/10.1051/mmnp/201510608 | |
| Published online | 02 October 2015 | |
A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding
Department of Mathematics, University of Chester
Thornton Science Park Pool Lane, Ince, Chester
CH2 4NU,
UK
⋆ Corresponding author. E-mail: n.kavallaris@chester.ac.uk,
y.yan@chester.ac.uk
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.
Mathematics Subject Classification: Primary 65N15 / 65N30 / Secondary 35K55 / 35K65 / 35R35
Key words: Non-local / degenerate parabolic equation / moving boundary / stability / error estimates / Chernoff formula / resistance spot welding
© EDP Sciences, 2015
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