A robust cut-cell finite element method for Poisson's equation in three dimensions

被引：0

作者：

Li, Donghao ^{[1
]}

Papadopoulos, Panayiotis ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USA

来源：

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2024年

关键词：

Cartesian grid; cut cell; finite element method; Poisson's equation; rate of convergence; small-cell problem; EMBEDDED-BOUNDARY METHOD; EXTENSION;

D O I：

10.1002/nme.7577

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This article documents a cut-cell finite element method for solving Poisson's equation in smooth three-dimensional domains using a uniform, Cartesian axis-aligned grid. Neumann boundary conditions are imposed weakly by way of a Delaunay triangulation, while Dirichlet boundary conditions are imposed strongly using a projection method. A set of numerical simulations demonstrates the proposed method is robust and preserves the asymptotic rate of convergence expected of corresponding body-fitted methods.

引用

页数：20

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