用不完全信息求解 PDEs

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-05-30 DOI:10.1137/23m1546671

Peter Binev, Andrea Bonito, Albert Cohen, Wolfgang Dahmen, Ronald DeVore, Guergana Petrova

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 3 期第 1278-1312 页，2024 年 6 月。摘要。我们考虑了在没有足够信息确定唯一解的情况下数值逼近偏微分方程 (PDE) 解的问题。我们的主要例子是泊松边界值问题，当边界数据未知时，我们只能观察解的有限多个线性测量值。我们将这种情况视为最优恢复问题，并为其求解开发了理论和数值算法。我们采用的主要工具是推导和近似这些函数的里厄斯表示数，并将其与谐函数的相关希尔伯特空间联系起来。

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Solving PDEs with Incomplete Information

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1278-1312, June 2024.
Abstract. We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when the boundary data is unknown and instead one observes finitely many linear measurements of the solution. We view this setting as an optimal recovery problem and develop theory and numerical algorithms for its solution. The main vehicle employed is the derivation and approximation of the Riesz representers of these functionals with respect to relevant Hilbert spaces of harmonic functions.

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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.