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Least square finite volume particle method for solving PDEs.

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Bibliographic Details
Title: Least square finite volume particle method for solving PDEs.
Authors: Zhang, Zhen1 (AUTHOR), Liu, Xiaoxing1 (AUTHOR) liuxx85@mail.sysu.edu.cn
Source: Computers & Mathematics with Applications. May2026, Vol. 210, p137-152. 16p.
Subjects: Finite volume method, Particle methods (Numerical analysis), Numerical analysis, Taylor's series, Partial differential equations, Meshfree methods, Least squares, Gaussian quadrature formulas
Abstract: Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2026.02.020