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| 摘要: |
| 本文研究了二维扩散方程九点格式中节点辅助未知量的插值问题.利用多点通量逼近的边未知量插值算法和一个特殊的极限技巧，获得了节点辅助未知量的一个新的插值算法，并在给定假设下严格分析了该算法中局部线性系统的可解性.新算法满足线性精确准则，具有较高的精度. |
| 关键词: 扩散方程 九点格式 节点未知量插值 线性精确 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金资助（11271053；11671313）. |
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| A NEW NODAL INTERPOLATION ALGORITHM IN NINE POINT SCHEME FOR DIFFUSION PROBLEMS |
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DONG Cheng,WU Ji-ming
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| Abstract: |
| In this paper, we discuss the interpolation problem for nodal auxiliary unknowns in nine point scheme for 2D diffusion problems. By applying a special limit technique to the edge interpolation algorithm in multipoint flux approximation, we obtain a new nodal interpolation algorithm. Moreover, the solvability of the local system in the interpolation algorithm is analyzed rigorously under certain assumptions. The new algorithm satisfies linearity preserving criterion and has a second-order accuracy. |
| Key words: diffusion equation nine point scheme nodal interpolation algorithm linearity preserving |
