Oseen方程的嵌入不连续伽辽金法

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-09-21 DOI:10.1051/m2an/2021059

Yongbin Han, Yanren Hou

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引用次数: 1

摘要

本文给出了Oseen方程的嵌入式不连续伽辽金方法的先验误差估计。证明了l2 (Ω)范数中的速度误差在扩散主导下具有收敛阶为k +1的最优误差界，其中常数依赖于雷诺数(或ν−1)，在对流主导下具有拟最优收敛阶为k +1 / 2的Reynolds-鲁棒误差界。这里，k是速度空间的多项式阶。此外，我们还证明了压力的最优误差估计。最后，我们进行了一些数值实验来证实我们的分析结果。

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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An embedded discontinuous Galerkin method for the Oseen equations

In this paper, the a prior error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the L 2 (Ω) norm, has an optimal error bound with convergence order k + 1, where the constants are dependent on the Reynolds number (or ν − 1 ), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order k +1 / 2. Here, k is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.