伯努利原理
数学
涡度
估计员
分段
有限元法
先验与后验
应用数学
数学分析
规范(哲学)
稳健性(进化)
涡流
物理
机械
统计
基因
认识论
热力学
哲学
生物化学
化学
法学
政治学
作者
Verónica Anaya,David Mora,Amiya K. Pani,Ricardo Ruiz-Baier
出处
期刊:Journal of Numerical Mathematics
[De Gruyter]
日期:2021-08-26
卷期号:30 (3): 209-230
标识
DOI:10.1515/jnma-2021-0053
摘要
Abstract A variational formulation is analysed for the Oseen equations written in terms of vorticity and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A finite element method is also proposed, consisting in equal-order Nédélec finite elements and piecewise continuous polynomials for the vorticity and the Bernoulli pressure, respectively. The a priori error analysis is carried out in the L 2 -norm for vorticity, pressure, and velocity; under a smallness assumption either on the convecting velocity, or on the mesh parameter. Furthermore, an a posteriori error estimator is designed and its robustness and efficiency are studied using weighted norms. Finally, a set of numerical examples in 2D and 3D is given, where the error indicator serves to guide adaptive mesh refinement. These tests illustrate the behaviour of the new formulation in typical flow conditions, and also confirm the theoretical findings.
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