A monotone finite element scheme for convection-diffusion equations

Xu, Jinchao; Zikatanov, Ludmil

doi:10.1090/S0025-5718-99-01148-5

A monotone finite element scheme for convection-diffusion equations
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by Jinchao Xu and Ludmil Zikatanov PDF

Math. Comp. 68 (1999), 1429-1446 Request permission

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 $M$-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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