基于变分公式和正则方形网格的节点鬼影法求解二维任意域上的椭圆问题

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Clarissa Astuto , Daniele Boffi , Giovanni Russo , Umberto Zerbinati
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引用次数: 0

摘要

本文重点研究了具有Dirichlet和混合边界条件的椭圆型偏微分方程的数值解,特别解决了不规则区域所带来的挑战。有限元法(FEM)和有限差分法(FDM)都面临着处理任意域问题的困难。本文介绍了一种基于变分公式的节点对称虚影法,结合了有限元法和FDM法的优点。该方法在结构网格上采用双线性有限元,并提供了详细的实现描述。并给出了严格的先验收敛率分析。在一维和二维空间上的数值实验验证了该方法的收敛速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions
This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method (FEM) and finite difference method (FDM), face difficulties in dealing with arbitrary domains. The paper introduces a novel nodal symmetric ghost method based on a variational formulation, which combines the advantages of FEM and FDM. The method employs bilinear finite elements on a structured mesh and provides a detailed implementation description. A rigorous a priori convergence rate analysis is also presented. The convergence rates are validated with many numerical experiments, in both one and two space dimensions.
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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