Convergence analysis of a fast virtual element method for coupled Darcy flows in fractured porous media on general polygonal meshes

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-08-12 DOI:10.1016/j.camwa.2025.08.002

Peixuan Wu, Yang Wang

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引用次数: 0

Abstract

In this article, we propose a novel two-grid discretization for the approximation of coupled Darcy flows in fractured porous media on general polygonal meshes. The Finite Element Method (FEM) is used to discreting the reduced fracture equation, and the Virtual Element Method (VEM) is applied to the matrix equation. The core of our fast VEM lies in the utilization of two meshes with distinct grid sizes. On the coarse grid, we solve the original coupled problem, and subsequently, we employ the coarse grid solution to decouple the equations on the finer grid. Optimal error estimates in

L^{2}

and semi-

H^{1}

norm for the VEM solution and semi-

H^{1}

norm for the fast VEM solution are rigorously provided, respectively, which shows our algorithm is capable of achieving asymptotically optimal estimation while significantly minimizing computational expenses.

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一般多边形网格上裂隙多孔介质中耦合达西流动的快速虚元法收敛性分析

在本文中，我们提出了一种新的双网格离散方法，用于在一般多边形网格上近似裂缝多孔介质中耦合达西流动。采用有限元法对断裂简化方程进行离散，采用虚元法对矩阵方程进行求解。我们快速VEM的核心在于利用两个网格大小不同的网格。首先在粗网格上求解原耦合问题，然后在细网格上利用粗网格解耦方程。严格地给出了VEM解的L2范数和半h1范数的最优误差估计，以及快速VEM解的半h1范数的最优误差估计，这表明我们的算法能够在显著降低计算费用的同时实现渐近最优估计。

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

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).