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

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 c...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 383; p. 113875
Main Authors: Pande, Sushrut, Papadopoulos, Panayiotis, Babuška, Ivo
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2021
Elsevier BV
Subjects:
Asymptotic methods
Boundary conditions
Cartesian coordinates
Cartesian grid
Convergence
Cut-cell
Dirichlet problem
Domains
Finite element analysis
Finite element method
Poisson equation
Poisson’s equation
Finite element method
Cartesian grid
Poisson’s equation
Cut-cell
Convergence
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary: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. •A finite element method suitable for two-dimensional digitally-generated voxel-based meshes, e.g., using microCT.•A simple procedure that enables the accurate and stable depiction of curved boundaries for domains embedded in a Cartesian grid.•The algorithm is shown to preserve the asymptotic theoretical convergence rate of unstructured body-fitted meshes on a number of numerical tests.•A simple and efficient method that can be easily implemented in existing codes.•Formal convergence proof available in one-dimensional case.•A method that may be generalized to three dimensional meshes.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.113875