对于R2中Navier-Stokes方程的有限元素方法的统一误差估计,初始数据为L2
Shuyan Ren1, Kun Wang2, Xinlong Feng1
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
Entropy (Basel, Switzerland)
|May 27, 2023
概括
本研究分析了纳维埃-斯托克斯方程的有限元素方法,其初始数据不那么平滑. 我们为速度和压力建立了统一的时间误差极限,改进了流体动力学的数值分析.
科学领域:
- 计算流体动力学的流体动力学.
- 数字分析 数字分析
- 部分微分方程 部分微分方程
背景情况:
- 纳维埃-斯托克斯方程控制流体运动,但很难用数值来解决.
- 解决方案可能是单一的,初始数据不平滑,复杂分析.
- 有限元素方法被广泛用于近似解决方案.
研究的目的:
- 用L2初始数据研究纳维埃-斯托克斯方程的有限元素方法.
- 为了获得速度和压力的统一时间误差估计.
- 为了应对因初始数据流性差而造成的单一解决方案所带来的挑战.
主要方法:
- 应用有限元素方法.
- 使用整体技术进行分析.
- 使用负面规范中的估计.
- 对溶液强加一个独特性条件.
主要成果:
- 该溶液在t在[0,1]中的H1规范中表现出奇点.
- 统一的时间最佳误差极限是根据H1-norm.中的速度推断出来的.
- 统一的时间最佳误差极限被推断为压力在L2-norm.
结论:
- 有限元素方法可以有效地处理纳维埃-斯托克斯问题,初始数据不那么顺.
- 导出的误差极限为数值近似提供了理论上的保证.
- 这项工作促进了对单一流体动力学问题的数值方法的理解.
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