Abstract
SummaryThis 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.
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