带阻尼平稳Navier-Stokes方程的牛顿迭代双网格算法

IF 0.8 3区数学 Q2 MATHEMATICS

Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI:10.1007/s11464-021-0018-6

Bo Zheng, Yueqiang Shang

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引用次数: 0

摘要

在有限元离散化的基础上，提出了一种新的基于牛顿迭代的两网格算法来求解具有非线性阻尼项的平稳Navier-Stokes方程。本文提出的两网格算法分为三步:第一步求解一个小的非线性粗网格问题，第二步和第三步分别求解两个基于牛顿迭代的线性细网格问题，这两个问题具有相同的刚度矩阵，只是右侧不同。我们分析了该算法的稳定性，并证明了该算法得到的近似解的收敛速度。数值结果表明，该算法的有效性，与常用的双网格算法相比，大大提高了近似解的精度。

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A New Two-grid Algorithm Based on Newton Iteration for the Stationary Navier–Stokes Equations with Damping

Based on finite element discretization, a new two-grid algorithm based on Newton iteration is proposed to solve the stationary Navier–Stokes equations with nonlinear damping term. The proposed new two-grid algorithm consists of three steps: in the first step, we solve one small nonlinear coarse grid problem, and then, in the second and third steps, we solve two linear fine grid problems based on Newton iteration which have the same stiffness matrices with only different right-hand sides. We analyze stability of the present algorithm and prove rate of convergence of the approximate solutions obtained from the algorithm. Numerical results are given to demonstrate the effectiveness of the present algorithm, showing that our algorithm greatly improves the accuracy of the approximate solutions comparable to that of the usual two-grid algorithm.

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来源期刊

Frontiers of Mathematics in China MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

703

审稿时长

6-12 weeks

期刊介绍： Frontiers of Mathematics in China provides a forum for a broad blend of peer-reviewed scholarly papers in order to promote rapid communication of mathematical developments. It reflects the enormous advances that are currently being made in the field of mathematics. The subject areas featured include all main branches of mathematics, both pure and applied. In addition to core areas (such as geometry, algebra, topology, number theory, real and complex function theory, functional analysis, probability theory, combinatorics and graph theory, dynamical systems and differential equations), applied areas (such as statistics, computational mathematics, numerical analysis, mathematical biology, mathematical finance and the like) will also be selected. The journal especially encourages papers in developing and promising fields as well as papers showing the interaction between different areas of mathematics, or the interaction between mathematics and science and engineering.