A monotone finite element scheme for convection-diffusion equations
A monotone finite element scheme for convection-diffusion equations
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DOI：
10.1090/s0025-5718-99-01148-5
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发表时间：
1999-10
期刊：
影响因子：
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通讯作者：
Jinchao Xu;L. Zikatanov
中科院分区：
文献类型：
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作者：
Jinchao Xu;L. Zikatanov
本文给出了一种简单的技术，通过对单元边缘上的偏微分方程系数进行适当平均，来构造和分析任意空间维度的对流扩散问题的一类有限元离散化。所得到的有限元刚度矩阵是在对基础（通常是非结构化）有限元网格进行某种温和假设的情况下的 M 矩阵。因此，所提出的边缘平均有限元方案对于对流主导问题的离散化特别有意义。该方案变分公式简单，易于分析，也适用于通量变量相对平滑的问题。给出了一些简单的数值例子来证明其对于对流主导问题的有效性。
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.