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Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

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  • Sidi Ammi, Moulay Rchid
  • Torres, Delfim F.M.

Abstract

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order error estimate. The full discrete backward Euler method and the Crank–Nicolson–Galerkin scheme are also considered. Finally, a simple algorithm for solving the fully discrete problem is proposed.

Suggested Citation

  • Sidi Ammi, Moulay Rchid & Torres, Delfim F.M., 2008. "Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 291-300.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:2:p:291-300
    DOI: 10.1016/j.matcom.2007.08.013
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    Cited by:

    1. Moulay Rchid Sidi Ammi & Delfim F. M. Torres, 2013. "Existence of Three Positive Solutions to Some p -Laplacian Boundary Value Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, February.

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