半线性椭圆方程的Dirichlet-Neumann交替方法的收敛性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-10-14 DOI:10.1137/24m1703550

Emil Engström

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第5期，2133-2154页，2025年10月。摘要。Dirichlet-Neumann交替法是求解无交叉点无重叠区域分解的常用方法，该方法在求解线性椭圆型方程时得到了广泛的研究。然而，对于非线性椭圆型方程，只有在一个空间维度上的某些特定情况下才有收敛结果。因此，本文的目的是证明Dirichlet-Neumann交替方法在二维和三维空间的Lipschitz连续域上收敛于一类半线性椭圆方程。这是通过首先证明Hilbert空间中非线性迭代的收敛性的一个新结果，然后将该结果应用于Dirichlet-Neumann交替方法的steklov - poincar公式来实现的。

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Convergence of the Dirichlet–Neumann Alternating Method for Semilinear Elliptic Equations

SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 2133-2154, October 2025.
Abstract. The Dirichlet–Neumann alternating method is a common domain decomposition method for nonoverlapping domain decompositions without cross-points, and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are only convergence results for some specific cases in one spatial dimension. The aim of this manuscript is therefore to prove that the Dirichlet–Neumann alternating method converges for a class of semilinear elliptic equations on Lipschitz continuous domains in two and three spatial dimensions. This is achieved by first proving a new result on the convergence of nonlinear iterations in Hilbert spaces and then applying this result to the Steklov–Poincaré formulation of the Dirichlet–Neumann alternating method.

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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.