Cell boundary element methods for convection-diffusion equations

Youngmok Jeon; Eun-Jae Park

doi:10.3934/cpaa.2006.5.309

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2006, Volume 5, Issue 2: 309-319. Doi: 10.3934/cpaa.2006.5.309

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Cell boundary element methods for convection-diffusion equations

Youngmok Jeon^1, and
Eun-Jae Park^2,

1.
Department of Mathematics, Ajou University, Suwon 443-749
2.
Department of Mathematics, Yonsei University, Seoul 120-749

Received: January 31, 2005

Revised: April 30, 2005

Published: May 2006

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Abstract

The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the orientation of the mesh we could obtain a stable non-oscillatory numerical scheme. We also consider a local basis (wind-oriented element) which incorporates the wind direction. Numerical examples are presented to compare various elements with the existing method such as the streamline diffusion method (SUPG).

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Mathematics Subject Classification: Primary: 65N30, 65N38, 65N50; Secondary: 76.

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