三维-一维系统的非连续伽勒金方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-08-02 DOI:10.1137/23m1627390

Rami Masri, Miroslav Kuchta, Beatrice Riviere

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 4 期第 1814-1843 页，2024 年 8 月。摘要。我们提出并分析了三维一维耦合系统的非连续 Galerkin（dG）近似方法，该方法模拟了三维域中的扩散，该三维域包含一个缩小到其一维中心线的小包体。通过推导后验误差估计和用合适的提升算子定义的残差边界，确定了对稳态问题弱解的收敛性。对于随时间变化的问题，还提出并分析了后向欧拉 dG 公式。此外，我们还为嵌入三维域的网络提出了一种 dG 方法，该方法在分岔点上具有局部质量保证，直至跃迁项。理想化几何中的数值示例描绘了我们的理论发现，而现实一维网络中的模拟则显示了我们方法的稳健性。

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Discontinuous Galerkin Methods for 3D–1D Systems

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1814-1843, August 2024.
Abstract. We propose and analyze discontinuous Galerkin (dG) approximations to 3D−1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state problem is established via deriving a posteriori error estimates and bounds on residuals defined with suitable lift operators. For the time-dependent problem, a backward Euler dG formulation is also presented and analyzed. Further, we propose a dG method for networks embedded in 3D domains, which is, up to jump terms, locally mass conservative on bifurcation points. Numerical examples in idealized geometries portray our theoretical findings, and simulations in realistic 1D networks show the robustness of our method.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.