This article is cited in 1 paper

Application of non-conforming finite elements for solving problems of diffusion and advection

V. I. Kuzin^ab, V. V. Kravtchenko<sup>a

a</sup> Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University, Novosibirsk

Abstract: The object of this paper is non-conforming finite elements and non-conforming finite element schemes for solving the diffusion-advection equation. This investigation is aimed at finding new schemes for solving parabolic equations. The method of the study is a finite element method, variational-difference schemes, tests. Two types of schemes are examined: the one is obtained with the help of the Bubnov–Galerkin method from a poor problem definition (non-monotone scheme) and the other one is a monotone up-stream type scheme, obtained from an approximate poor problem definition with a special approximation of skew-symmetric terms.

Key words: non-conforming finite elements, diffusion and advection equation, finite element method, Bubnov–Galerkin method, up-stream type scheme.

UDC: 519.6+532.5

Received: 17.03.2009
Revised: 15.04.2009

 English version: Numerical Analysis and Applications, 2010, 3:1, 39–51

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