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 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.