A robust cut‐cell finite element method for Poisson's equation in three dimensions
Copyright policy )A robust cut‐cell finite element method for Poisson's equation in three dimensions
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.
- University of California, Berkeley United States
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, finite element method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, cut cell, Cartesian grid, small-cell problem, Poisson's equation, Spline approximation, Numerical interpolation, Tilings in \(n\) dimensions (aspects of discrete geometry), rate of convergence
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, finite element method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, cut cell, Cartesian grid, small-cell problem, Poisson's equation, Spline approximation, Numerical interpolation, Tilings in \(n\) dimensions (aspects of discrete geometry), rate of convergence
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