基于对偶性的西格诺里尼问题误差控制

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Numerical Analysis Pub Date : 2024-07-23 DOI:10.1137/22m1534791

Ben S. Ashby, Tristan Pryer

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 4 期第 1687-1712 页，2024 年 8 月。摘要本文研究了 Signorini 问题的符合片断线性有限元近似的后验边界。我们证明了[math]中残差类型的新的严格后验估计，适用于两个空间维度的[math]。这一新的分析分别处理离散化误差的正负部分，需要一个新颖的符号和边界保留插值，并证明其具有最佳近似特性。对于任意[math]问题，估计值依赖于[math]中关于该问题的尖锐对偶稳定性结果。我们总结了大量旨在测试估计器稳健性的数值实验，以验证理论。

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Duality-Based Error Control for the Signorini Problem

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1687-1712, August 2024.
Abstract. In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in [math], for [math] in two spatial dimensions. This new analysis treats the positive and negative parts of the discretization error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in [math] for any [math]. We summarize extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.