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Zbl 0979.78023
Allegretto, Walter; Lin, Yanping; Zhou, Aihui
A box scheme for coupled systems resulting from microsensor thermistor problems. (English)
[J] Dyn. Contin. Discrete Impulsive Syst. 5, No.1-4, 209-223 (1999). ISSN 1201-3390

Summary: A box approximation scheme is proposed using the lumped mass numerical integration technique on piecewise linear finite element spaces for a coupled nonlinear thermistor system. Existence and uniqueness of the approximation solution are proved via a fixed point theorem, and an $H^1$-error analysis is presented.

MSC 2000:: *78A55 Technical appl. of optics and electromagnetic theory
65N12 Stability and convergence of numerical methods (BVP of PDE)
78M25 Numerical methods in optics
35K65 Parabolic equations of degenerate type

Keywords: electric heating; existence; box approximation scheme; lumped mass numerical integration; piecewise linear finite element spaces; coupled nonlinear thermistor system; uniqueness

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