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Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem. (English) Zbl 1149.65083

The authors study the spatially semidiscrete piecewise linear finite element method for the nonlinear parabolic problem

u/t-·(k(u)u)=λf(u)/ Ω f (u) d x 2

in Ω×(0,t ¯), u=0 on Ω×(0,t ¯), u(0)=u 0 in Ω, where Ω is a bounded domain in 2 , t ¯ a positive number, f and k given functions from to , λ>0. This parabolic problem describes the temperature profile of a thermistor device with electrical resistivity f. The full discrete backward Euler method and the Crank-Nicolson-Galerkin scheme are also considered. An algorithm for solving the fully discrete problem is proposed but no numerical results are presented.

65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M20Method of lines (IVP of PDE)
35K55Nonlinear parabolic equations
65M06Finite difference methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
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