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Journal of Applied Mathematics and Computing

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01.10.2013 | Original Research

A coupling method based on new MFE and FE for fourth-order parabolic equation

verfasst von: Yang Liu, Zhichao Fang, Hong Li, Siriguleng He, Wei Gao

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2013

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Abstract

In this article, a coupling method of new mixed finite element (MFE) and finite element (FE) is proposed and analyzed for fourth-order parabolic partial differential equation. First, the fourth-order parabolic equation is split into the coupled system of second-order equations. Then, an equation is solved by finite element method, the other equation is approximated by the new mixed finite element method, whose flux belongs to the square integrable space replacing the classical H(div;Ω) space. The stability for fully discrete scheme is derived, and both semi-discrete and fully discrete error estimates are obtained. Moreover, the optimal a priori error estimates in L ² and H ¹-norm for both the scalar unknown u and the diffusion term γ and a priori error estimate in (L ²)²-norm for its flux σ are derived. Finally, some numerical results are provided to validate our theoretical analysis.

Vorheriger Artikel An impulsive diffusion predator-prey system in three-species with Beddington-DeAngelis response

Nächster Artikel Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

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Titel: A coupling method based on new MFE and FE for fourth-order parabolic equation
verfasst von: Yang Liu
Zhichao Fang
Hong Li
Siriguleng He
Wei Gao
Publikationsdatum: 01.10.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2013
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-013-0662-4

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