Optimal error bound and regularization methods for identifying an unknown source in an advection-dispersion equation

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-22 DOI:10.1016/j.cam.2026.117461

Hanghang Wu , Hongqi Yang

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引用次数: 0

Abstract

We consider the problem of identifying the source term in an advection-dispersion equation based on given terminal data. It is shown that this is an ill-posed problem. The optimal error bound of the problem under certain source conditions is given. Then, the mollification regularization method and the Fourier regularization method are used to solve the problem respectively. Under the selection rules of a-priori and a-posteriori regularization parameters, we derive the a-priori and a-posteriori error estimates. From the theoretical derivation, it can be seen that the error estimates obtained by both regularization methods do not exhibit saturation effects, and the a-posteriori error estimate obtained by using the Fourier regularization is optimal. Finally, numerical experiments are conducted to demonstrate the effectiveness and stability of the proposed regularization methods. Additionally, comparisons between the two regularization methods are presented, along with the conclusions drawn from these comparisons.

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平流色散方程中未知源识别的最优误差界和正则化方法

我们考虑了基于给定终端数据的平流-色散方程中源项的识别问题。证明了这是一个不适定问题。在一定的源条件下，给出了问题的最优误差界。然后分别采用柔化正则化方法和傅立叶正则化方法求解该问题。在先验和后验正则化参数的选择规则下，推导了先验和后验误差估计。从理论推导可以看出，两种正则化方法得到的误差估计都不存在饱和效应，采用傅里叶正则化方法得到的后验误差估计是最优的。最后，通过数值实验验证了所提正则化方法的有效性和稳定性。此外，提出了两种正则化方法之间的比较，以及从这些比较中得出的结论。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.