Two stabilized finite element methods based on local polynomial pressure projection for the steady-state Navier–Stokes–Darcy problem

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2025-08-15 DOI:10.1016/j.finel.2025.104420

Liyun Zuo , Guangzhi Du

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引用次数: 0

Abstract

This study presents two stabilized finite element methods based on local polynomial pressure projections for the mixed steady-state Navier–Stokes–Darcy problem by utilizing the equal order finite element pairs, the

P_{1}

P_{1}

P_{1}

and

P_{2}

P_{2}

P_{2}

element pairs, for approximating the fluid velocity, kinematic pressure and dynamic pressure, respectively. The presented stabilized methods possess many chief characteristics, for instance, parameter free, simple calculation, element level implementation. The optimal error estimates are established. Finally, some comprehensively numerical tests are reported to examine the efficiency and robustness of the proposed algorithms.

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求解稳态Navier-Stokes-Darcy问题的两种基于局部多项式压力投影的稳定有限元方法

针对混合稳态Navier-Stokes-Darcy问题，利用等阶有限元对P1-P1-P1和P2-P2-P2单元对分别逼近流体速度、运动压力和动压力，提出了两种基于局部多项式压力投影的稳定有限元方法。所提出的稳定方法具有无参数、计算简单、单元级实现等主要特点。建立了最优误差估计。最后，通过数值实验验证了所提算法的有效性和鲁棒性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.