Comptes Rendus
Numerical analysis, Partial differential equations
Finite element error estimates for a mixed degenerate parabolic model
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 431-438.

The aim of this note is to deduce error estimates for a fully-discrete finite element method approximation of a kind of degenerate mixed parabolic equations. The obtained results consider regularity assumptions about the main variable according to the degenerate character of the problem, given by the term involving the time-derivative, which is represented with a non-invertible linear operator R. We show two different approaches to obtain the error estimates. The first one needs to introduce an extension operator of R and the second one requires to add a new ellipticity property for this operator. These error estimates can be applied to analyze the fully-discrete finite element method approximation of an eddy current model.

Le but de cette note est de déduire des estimations d’erreur pour une approximation par la méthode des éléments finis entièrement discrets d’un type d’équations paraboliques mixtes dégénérées. Les résultats obtenus considèrent des hypothèses de régularité sur la variable principale selon le caractère dégénéré du problème, donné par le terme impliquant la dérivée temporelle, qui est représentée par un opérateur linéaire non inversible R. Nous présentons deux approches différentes pour obtenir les estimations d’erreur. La première nécessite d’introduire un opérateur d’extension de R et la seconde nécessite d’ajouter une nouvelle propriété d’ellipticité pour cet opérateur. Ces estimations d’erreur peuvent être appliquées pour analyser l’approximation par la méthode des éléments finis entièrement discrets d’un modèle de courants de Foucault.

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DOI: 10.5802/crmath.308
Classification: 65N30, 35K65, 78M10
Ramiro Miguel Acevedo Martínez 1; Christian Camilo Gómez Mosquera 1

1 Departamento de Matemáticas, Universidad del Cauca, Popayán, Colombia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Finite element error estimates for a mixed degenerate parabolic model},
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Ramiro Miguel Acevedo Martínez; Christian Camilo Gómez Mosquera. Finite element error estimates for a mixed degenerate parabolic model. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 431-438. doi : 10.5802/crmath.308. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.308/

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