A CUT-CELL FINITE ELEMENT METHOD FOR POISSON’S EQUATION ON ARBITRARY PLANAR DOMAINS
S. Pande, P. Papadopoulos, and I. Babuška Computer Methods in Applied Mechanics and Engineering, 383, 113875, (2021).

Abstract
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.


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