A monotone finite element scheme for convection-diffusion equations |
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Authors: | Jinchao Xu Ludmil Zikatanov. |
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Affiliation: | Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 ; Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 |
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Abstract: | A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. As a consequence the proposed edge-averaged finite element scheme is particularly interesting for the discretization of convection dominated problems. This scheme admits a simple variational formulation, it is easy to analyze, and it is also suitable for problems with a relatively smooth flux variable. Some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems. |
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Keywords: | Convection dominated problems finite element method monotone schemes up-winding Scharfetter-Gummel discretization error bounds |
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