Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

Details Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

2007-09-02

arxiv.org/abs/0709.0129v1

Math. Comput. Simul. 77 (2008) 291--300. DOI: 10.1016/j.matcom.2007.08.013

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.matcom.2007.08.013

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.

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