Computational Unique Continuation with Finite Dimensional Neumann Trace

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-09-16 DOI:10.1137/24m164080x

Erik Burman, Lauri Oksanen, Ziyao Zhao

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 1986-2008, October 2025.
Abstract. We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative error estimates we prove Lipschitz stability of the unique continuation problem in the global [math]-norm. This stability is then leveraged to derive optimal a posteriori and a priori error estimates for a primal-dual stabilized finite element method.

查看原文本刊更多论文

有限维Neumann迹的计算唯一延拓

SIAM数值分析杂志，第63卷，第5期，1986-2008页，2025年10月。摘要。考虑椭圆型方程唯一延拓问题的有限元逼近，其中精确解的法向导数已知存在于有限维空间中。为了给出定量误差估计，我们证明了唯一连续问题在全局范数下的Lipschitz稳定性。然后利用这种稳定性推导出原始-对偶稳定有限元方法的最优后验和先验误差估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.