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

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.