用反问题估计近似误差，并给出一组数值解

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-01-02 DOI:10.1080/17415977.2021.2000604

A. Alekseev, A. Bondarev

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引用次数: 2

摘要

本文研究了在偏微分方程组离散化时出现的逐点逼近误差估计的反问题。我们分析了在同一网格上不同结构的数值算法得到的解集。将数值解之间的差值作为反问题的输入数据，用零阶Tikhonov正则化的变分语句提出反问题。给出了Edney-I和Edney-VI两种激波干涉模式下二维无粘可压缩流动的数值试验结果。给出了用数值解和解析解相减得到的估计误差和精确误差的比较。

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The estimation of approximation error using inverse problem and a set of numerical solutions

In this paper, we consider the inverse problem for the estimation of a point-wise approximation error occurring at the discretization of the system of partial differential equations. We analyse the set of the solutions, obtained by the numerical algorithms of the dissimilar structures on the same grid. The differences between the numerical solutions are used as the input data for the inverse problem, which is posed in the variational statement with the zero-order Tikhonov regularization. The numerical tests, performed for the two-dimensional inviscid compressible flows corresponding to Edney-I and Edney-VI shock wave interference modes, are provided. The comparison of the estimated error and the exact error, obtained by subtraction of numerical and analytic solutions, is presented.

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.