Abstract
This paper deals with the numerical analysis for a family of nonlinear degenerate parabolic problems. The model is spatially discretized using a finite element method; an implicit Euler scheme is employed for time discretization. We deduce sufficient conditions to ensure that the fully discrete problem has a unique solution and to prove quasi-optimal error estimates for the approximation. Finally, we propose a nonlinear degenerate parabolic problem that arises from electromagnetic applications in conductive nonlinear magnetic media and deduce its solubility and convergence by using the developed abstract theory, including some numerical results to confirm the obtained theoretical results.
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Open Access funding provided by Colombia Consortium. This work was partially supported by the University of Cauca through project VRI ID 5869. P. Navia was partially supported by Minciencias (Colombia) through the Bicentennial PhD Scholarship Program.
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Communicated by: Francesca Rapetti
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R. Acevedo, C. Gómez and P. Navia contributed equally to this work.
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Acevedo, R., Gómez, C. & Navia, P. Numerical analysis of nonlinear degenerate parabolic problems with application to eddy current models. Adv Comput Math 49, 64 (2023). https://doi.org/10.1007/s10444-023-10052-0
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DOI: https://doi.org/10.1007/s10444-023-10052-0
Keywords
- Nonlinear partial differential equation
- Degenerate parabolic equations
- Finite element method
- Error estimates
- Eddy current model