American Institute of Mathematical Sciences

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June  2006, 5(2): 309-319. doi: 10.3934/cpaa.2006.5.309

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, South Korea
2. 

Department of Mathematics, Yonsei University, Seoul 120-749, South Korea

Received  February 2005 Revised  May 2005 Published  March 2006

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).
Keywords: convection-diffusion equations, Dirichlet-to-Neumann map., cell boundary element method.
Mathematics Subject Classification: Primary: 65N30, 65N38, 65N50; Secondary: 7.
Citation: Youngmok Jeon, Eun-Jae Park. Cell boundary element methods for convection-diffusion equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 309-319. doi: 10.3934/cpaa.2006.5.309
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