### 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.

Original language | English (US) |
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Pages (from-to) | 1429-1446 |

Number of pages | 18 |

Journal | Mathematics of Computation |

Volume | 68 |

Issue number | 228 |

DOIs | |

State | Published - Oct 1999 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics