Group actions in function approximation spaces

函数逼近空间中的群动作

• 批准号: EP/H024018/1
• 负责人: Elizabeth Mansfield
• 金额: $ 37.28万
• 依托单位: University of Kent
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH024018%2F1
• 关键词: Group; actions; function; approximation; spaces

In 1987, Britain experienced a hurricane that was famously not predicted by the UK Met Office.The PI heard that mathematicians working at the Met Office decided, after due deliberation, that the reason was that the numerical code used to predict extreme weather had a particular subtle flaw: that a conservation law, known as potential vorticity, was not built into the computer code. This kind of conservation law is guaranteed by a famous theorem, proved by Emmy Noether in the early 1900's, which links the symmetries of the physical model directly to the conservation laws.The long term aim of the line of research of the project is to build such laws, exactly, intonumerical code that models physical systems. This involves first understanding how the physical symmetries, which are understood in terms of smooth actions on smooth spaces,are mapped into actions in discrete or digital spaces; actually, onto the approximate functions on such spaces used to model the smooth functions. The second part involves investigatinghow Noether's theorem transfers to the discrete case in a concrete and practical way.

1987 年，英国经历了一场著名的飓风，但英国气象局没有预测到这场飓风。PI 听说，在英国气象局工作的数学家经过深思熟虑后认为，原因是用于预测极端天气的数字代码有一个特别微妙的缺陷：计算机代码中没有内置称为位涡度的守恒定律。这种守恒定律得到 Emmy Noether 在 1900 年代初证明的著名定理的保证，该定理将物理模型的对称性直接与守恒定律联系起来。该项目研究方向的长期目标是将此类定律准确地构建为模拟物理系统的数值代码。这涉及首先了解物理对称性（通过平滑空间上的平滑动作来理解）如何映射到离散或数字空间中的动作；实际上，是在用于对平滑函数进行建模的此类空间上的近似函数上。第二部分涉及研究诺特定理如何以具体和实用的方式转移到离散情况。

项目成果

A Posteriori Analysis of Discontinuous Galerkin Schemes for Systems of Hyperbolic Conservation Laws

双曲守恒律系统不连续伽辽金格式的后验分析

• DOI: 10.1137/140970999
• 发表时间: 2015
• 期刊: SIAM Journal on Numerical Analysis
• 影响因子: 2.9
• 作者: Giesselmann J

Moving Frames and Noether's Conservation Laws - the General Case

移动框架和诺特守恒定律 - 一般情况

• 发表时间: 2016
• 期刊: Forum in Mathematics, Sigma
• 作者: Goncalves TMN

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

• DOI: 10.1007/s10543-015-0560-2
• 发表时间: 2014-05
• 期刊: BIT Numerical Mathematics
• 影响因子: 1.5
• 作者: J. Giesselmann;T. Pryer

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

• DOI: 10.1093/imanum/drv052
• 发表时间: 2014-05
• 期刊: arXiv: Numerical Analysis
• 作者: J. Giesselmann;T. Pryer

Noether's Conservation Laws: smooth and discrete cases

诺特守恒定律：平滑和离散的情况

• 发表时间: 2010
• 作者: Goncalves TMN