Geodesic
Application of non-conforming finite elements for solving problems of diffusion and advection
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 51-65

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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. 
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V. I. Kuzin; V. V. Kravtchenko. Application of non-conforming finite elements for solving problems of diffusion and advection. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 51-65. http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a4/