A cut-cell finite element method for Poisson's equation on arbitrary planar domains

DOI10.1016/j.cma.2021.113875zbMath1506.65223OpenAlexW3163007748MaRDI QIDQ2237297

Sushrut Pande, Panayiotis Papadopoulos, Ivo M. Babuška

Publication date: 27 October 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2021.113875

zbMATH Keywords

convergencefinite element methodPoisson's equationcut-cellcartesian grid

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (1)

An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries

Uses Software

• CutFEM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Immersed finite element method
• On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
• A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics
• The finite cell method for three-dimensional problems of solid mechanics
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• Numerical analysis of blood flow in the heart
• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis
• Modeling a no-slip flow boundary with an external force field
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• A fictitious domain method for Dirichlet problem and applications
• A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary
• The design and analysis of the generalized finite element method
• Flow patterns around heart valves: A numerical method
• An immersed discontinuous finite element method for Stokes interface problems
• A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources
• Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry
• CutFEM: Discretizing geometry and partial differential equations
• Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions
• IMMERSED BOUNDARY METHODS
• An efficient finite element method for embedded interface problems
• A discontinuous-Galerkin-based immersed boundary method
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• An Immersed Interface Method for Incompressible Navier--Stokes Equations
• A distributed Lagrange multiplier/fictitious domain method for particulate flows
• Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains
• A Cartesian grid embedded boundary method for the heat equation on irregular domains

This page was built for publication: A cut-cell finite element method for Poisson's equation on arbitrary planar domains