凸最小化问题混合高阶方法的离散弱对偶性

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-07-04 DOI:10.1137/23m1594534

Ngoc Tien Tran

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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 1492-1514 页，2024 年 8 月。摘要本文推导了凸最小化问题的典型混合高阶方法的离散对偶问题。离散主问题和对偶问题满足弱凸对偶性，在额外的平滑性假设条件下可得到具有收敛率的先验误差估计。这种对偶性适用于一般多面体网格和任意多项式离散度。本文提出了一种新颖的后处理方法，并允许使用初等二元技术对规则三角形简图进行后验误差估计。这激发了一种自适应网格细化算法，与统一网格细化相比，该算法性能更好。

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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Discrete Weak Duality of Hybrid High-Order Methods for Convex Minimization Problems

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1492-1514, August 2024.
Abstract. This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with convergence rates under additional smoothness assumptions. This duality holds for general polyhedral meshes and arbitrary polynomial degrees of the discretization. A novel postprocessing is proposed and allows for a posteriori error estimates on regular triangulations into simplices using primal-dual techniques. This motivates an adaptive mesh-refining algorithm, which performs better compared to uniform mesh refinements.

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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.