On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

IF 3.8 2区 数学 Q1 MATHEMATICS Journal of Numerical Mathematics Pub Date : 2020-06-01 DOI:10.1515/jnma-2019-0001
J. Chaskalovic, F. Assous
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Abstract

Abstract The aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.
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评价有限元精度的广义二项式定律:自适应网格细化的初步概率结果
摘要本文的目的是为相对有限元精度的研究提供新的视角。从可以从Bramble-Hilbert引理推导出的误差估计的几何解释开始,我们推导出一个概率律来评估相对精度,作为一个随机变量,在两个有限元Pk和Pm之间,k < m。我们扩展这个概率律来得到两个主要应用的累积概率律。第一个涉及一组网格,第二个是专门用于构成给定网格的简单体序列。这两个应用都可以被认为是应用概率方法进行自适应网格细化的第一步。
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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来源期刊
CiteScore
5.90
自引率
3.30%
发文量
17
审稿时长
>12 weeks
期刊介绍: The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.
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