• 论文 •

### 任意四边形网格上扩散问题的一个稳定九点格式

1. 中国工程物理研究院研究生院, 北京 100088
• 收稿日期:2018-10-29 出版日期:2019-03-15 发布日期:2019-03-15
• 基金资助:

国家自然科学基金（11871009，11771052）.

Hong Qi, Su Shuai. A STABLE NINE-POINT SCHEME FOR DIFFUSION PROBLEMS ON ARBITRARY QUADRILATERAL MESHES[J]. Journal of Numerical Methods and Computer Applications, 2019, 40(1): 51-67.

### A STABLE NINE-POINT SCHEME FOR DIFFUSION PROBLEMS ON ARBITRARY QUADRILATERAL MESHES

Hong Qi, Su Shuai

1. Graduate School of China Academy of Engineering Physics, Beijing 100088, China
• Received:2018-10-29 Online:2019-03-15 Published:2019-03-15

We propose and analyze a stable nine-point scheme for diffusion problems by applying a modified Q1 finite volume element method (mQ1-FVEM) to treat the vertex unknowns. Based on the theoretical results of the mQ1-FVEM and a simple discrete functional technique, the stability result and error estimate of the resulting nine-point scheme both in H1 norm are obtained under a standard and weak geometric assumption. Our proposed scheme does not possess the so-called numerical heat-barrier issue suffered by many existing cell-centered or hybrid schemes. But, we need to solve two linear algebraic systems. Numerical experiments are also presented to show the efficiency of the proposed scheme and validate the theoretical analysis.

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