对流主导扩散问题的超局部正交分解

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Francesca Bonizzoni, Philip Freese, Daniel Peterseim
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引用次数: 0

摘要

本文提出了一种新颖的多尺度方法,用于解决大佩克莱特数条件下对流主导的扩散问题。该方法将解算子应用于任意粗网格上的片断常数右边,定义了一个具有良好近似特性的有限维粗安萨兹空间。对于一些相关的误差度量,包括(L^2)-norm,Galerkin投影到这个广义有限元空间甚至可以得到(varepsilon)独立的误差边界,(varepsilon)是奇异扰动参数。通过构建近似局部基础,该方法成为一种新颖的多尺度方法,与超局部正交分解(SLOD)的精神一脉相承。基础局部化引起的误差可以通过后验方法进行估计。与现有的多尺度方法相比,数值实验表明,即使在大网格贝克莱特数的欠分辨机制下,也没有预渐近效应,收敛性很强。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Super-localized orthogonal decomposition for convection-dominated diffusion problems

Super-localized orthogonal decomposition for convection-dominated diffusion problems

This paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coarse mesh, which defines a finite-dimensional coarse ansatz space with favorable approximation properties. For some relevant error measures, including the \(L^2\)-norm, the Galerkin projection onto this generalized finite element space even yields \(\varepsilon \)-independent error bounds, \(\varepsilon \) being the singular perturbation parameter. By constructing an approximate local basis, the approach becomes a novel multi-scale method in the spirit of the Super-Localized Orthogonal Decomposition (SLOD). The error caused by basis localization can be estimated in an a posteriori way. In contrast to existing multi-scale methods, numerical experiments indicate \(\varepsilon \)-robust convergence without pre-asymptotic effects even in the under-resolved regime of large mesh Péclet numbers.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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