Stability and Convergence of HDG Schemes under Minimal Regularity

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-09-25 DOI:10.1137/23m1612846

Jiannan Jiang, Noel J. Walkington, Yukun Yue

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 2048-2071, October 2025.
Abstract. Convergence and compactness properties of approximate solutions to elliptic partial differential equations computed with the hybridized discontinuous Galerkin (HDG) scheme of Cockburn, Gopalakrishnan, and Sayas (Math. Comp., 79 (2010), pp. 1351–1367) are established. While it is known that solutions computed using this scheme converge at optimal rates to smooth solutions, this does not establish the stability of the method or convergence to solutions with minimal regularity. The compactness and convergence results show that the HDG scheme can be utilized for the solution of nonlinear problems and linear problems with nonsmooth coefficients on domains with reentrant corners.

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最小正则性条件下HDG格式的稳定性和收敛性

SIAM数值分析杂志，第63卷，第5期，2048-2071页，2025年10月。摘要。用Cockburn， Gopalakrishnan和Sayas的杂交不连续Galerkin （HDG）格式计算椭圆型偏微分方程近似解的收敛性和紧性。Comp., 79 (2010), pp. 1351-1367)建立。虽然已知使用该格式计算的解以最优速率收敛到光滑解，但这并不能确定该方法的稳定性或收敛到具有最小规则性的解。紧凑性和收敛性结果表明，HDG格式可用于求解具有可重入角域上的非线性和非光滑系数线性问题。

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

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.