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Fully-discrete finite element approximation for a family of degenerate parabolic problems

    Ramiro Acevedo   Affiliation
    ; Christian Gómez   Affiliation
    ; Bibiana López-Rodríguez   Affiliation

Abstract

The aim of this work is to show an abstract framework to analyze the numerical approximation by using a finite element method in space and a BackwardEuler scheme in time of a family of degenerate parabolic problems. 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 show a degenerate parabolic problem which arises from electromagnetic applications and deduce its well-posedness and convergence by using the developed abstract theory, including numerical tests to illustrate the performance of the method and confirm the theoretical results.

Keyword : parabolic degenerate equations, parabolic-elliptic equations, finite element method, backward Euler scheme, fully-discrete approximation, error estimates, eddy current model

How to Cite
Acevedo, R., Gómez, C., & López-Rodríguez, B. (2022). Fully-discrete finite element approximation for a family of degenerate parabolic problems. Mathematical Modelling and Analysis, 27(1), 134–160. https://doi.org/10.3846/mma.2022.12846
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Feb 7, 2022
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