论准均匀矩形网格上拉普拉斯函数的 $Q^2$ 谱元法的单调性

IF 2.6 3区物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2024-01-01 DOI:10.4208/cicp.oa-2023-0206

Logan J. Cross, Xiangxiong Zhang

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引用次数: 0

摘要

离散拉普拉奇的单调性意味着离散最大值原则，而这在高阶方案中一般不成立。Q^2$谱元法已被证明在均匀矩形网格上具有单调性。在本文中，我们证明了在某些网格约束条件下，Q^2$谱元法在准均匀矩形网格上的单调性。特别是，我们提出了证明单调性的宽松洛伦兹条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes

The monotonicity of discrete Laplacian implies discrete maximum principle, which in general does not hold for high order schemes. The $Q^2$ spectral element method has been proven monotone on a uniform rectangular mesh. In this paper we prove the monotonicity of the $Q^2$ spectral element method on quasi-uniform rectangular meshes under certain mesh constraints. In particular, we propose a relaxed Lorenz’s condition for proving monotonicity.

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来源期刊

Communications in Computational Physics 物理-物理：数学物理

CiteScore

4.70

自引率

5.40%

发文量

审稿时长

9 months

期刊介绍： Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.