The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal Domain, I

Mohamed Farhloul (), Réda Korikache () and Luc Paquet ()
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Mohamed Farhloul: Université de Moncton, Département de mathématiques et de statistique Faculté des sciences
Réda Korikache: University of Valenciennes and Hainaut-Cambresis, LAMAV, EA 4015
Luc Paquet: University of Valenciennes and Hainaut-Cambresis, LAMAV, EA 4015

A chapter in Functional Analysis and Evolution Equations, 2007, pp 239-256 from Springer

Abstract: Abstract The aim of this paper is to prove a priori error estimates for the semi-discrete solution of the dual mixed method for the heat diffusion equation in a polygonal domain. Due to the geometric singularities of the domain, the solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces. In order to recapture the optimal order of convergence, the meshes are refined in an appropriate fashion near the reentrant corners of the domain.

Keywords: Dual mixed finite element method; heat diffusion equation; singularities; grids refinements; a priori error estimates (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_16

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DOI: 10.1007/978-3-7643-7794-6_16

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