4.7 Article

A cut-cell finite element method for Poisson's equation on arbitrary planar domains

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Publisher

ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2021.113875

Keywords

Finite element method; Cut-cell; Cartesian grid; Convergence; Poisson's equation

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This article introduces a cut-cell finite element method for solving Poisson's equation on two-dimensional domains of arbitrary shapes. Numerical experiments demonstrate that the method is stable and achieves the asymptotic convergence rates expected of unstructured body-fitted finite element methods.
This article introduces a cut-cell finite element method for Poisson's equation on arbitrarily shaped two-dimensional domains. The equation is solved on a Cartesian axis-aligned grid of 4-node elements which intersects the boundary of the domain in a smooth but arbitrary manner. Dirichlet boundary conditions are strongly imposed by a projection method, while Neumann boundary conditions require integration over a locally discretized boundary region. Representative numerical experiments demonstrate that the proposed method is stable and attains the asymptotic convergence rates expected of the corresponding unstructured body-fitted finite element method. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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