## 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.## References

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## Additional Information

**Jinchao Xu**- Affiliation: Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 228866
- Email: xu@math.psu.edu
**Ludmil Zikatanov**- Affiliation: Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- Email: ltz@math.psu.edu
- Received by editor(s): May 6, 1996
- Received by editor(s) in revised form: December 16, 1997
- Published electronically: May 20, 1999
- Additional Notes: The first author’s work was partially supported by NSF DMS94-03915-1 and NSF DMS-9706949 through Penn State, and by NSF ASC-92-01266 and ONR-N00014-92-J-1890 through UCLA

The second author’s work was partially supported by the Bulgarian Ministry of Education and Science Grant I–504/95, by NSF Grant Int-95–06184 and ONR-N00014-92-J-1890 through UCLA, and also by the Center for Computational Mathematics and Applications of Pennsylvania State University. - © Copyright 1999 American Mathematical Society
- Journal: Math. Comp.
**68**(1999), 1429-1446 - MSC (1991): Primary 65N30, 65N15
- DOI: https://doi.org/10.1090/S0025-5718-99-01148-5
- MathSciNet review: 1654022