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01.06.2020

Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations

verfasst von: El Houssaine Quenjel, Mazen Saad, Mustapha Ghilani, Marianne Bessemoulin-Chatard

Erschienen in: Calcolo | Ausgabe 2/2020

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Abstract

In this work, we carry out the convergence analysis of a positive DDFV method for approximating solutions of degenerate parabolic equations. The basic idea rests upon different approximations of the fluxes on the same interface of the control volume. Precisely, the approximated flux is split into two terms corresponding to the primal and dual normal components. Then the first term is discretized using a centered scheme whereas the second one is approximated in a non evident way by an upstream scheme. The novelty of our approach is twofold: on the one hand we prove that the resulting scheme preserves the positivity and on the other hand we establish energy estimates. Some numerical tests are presented and they show that the scheme in question turns out to be robust and efficient. The accuracy is almost of second order on general meshes when the solution is smooth.

Vorheriger Artikel On general matrix exponential discriminant analysis methods for high dimensionality reduction

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Titel: Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations
verfasst von: El Houssaine Quenjel
Mazen Saad
Mustapha Ghilani
Marianne Bessemoulin-Chatard
Publikationsdatum: 01.06.2020
Verlag: Springer International Publishing
Erschienen in: Calcolo / Ausgabe 2/2020
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-020-00367-5

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