A general fictitious domain method with immersed jumps and multilevel nested structured meshes

DOI10.1016/j.jcp.2007.01.026zbMath1122.65115OpenAlexW2004305317MaRDI QIDQ2381211

Isabelle Ramière, Philippe Angot, Michel Belliard

Publication date: 14 September 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.01.026

zbMATH Keywords

numerical resultsconvection-diffusion problemsDirichlet boundary conditionserror boundsNeumann boundary conditionsRobin boundary conditionselliptic problemsfictitious domain methodcell-centered finite volumeembedded boundary conditionsmultilevel local mesh refinementnon-conforming structured meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Cites Work

• Unnamed Item
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• A node-centered local refinement algorithm for Poisson's equation in complex geometries
• A penalization method to take into account obstacles in incompressible viscous flows
• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• Fictitious domain method for unsteady problems: application to electromagnetic scattering
• A model of fracture for elliptic problems with flux and solution jumps.
• A fictitious domain method for Dirichlet problems using mixed finite elements
• An overview of the immersed interface method and its applications
• A multilevel local mesh refinement projection method for low Mach number flows
• Error analysis of a fictitious domain method applied to a Dirichlet problem
• A fictitious domain method for Dirichlet problem and applications
• Wavelet and finite element solutions for the Neumann problem using fictitious domains
• A fictitious domain approach with spread interface for elliptic problems with general boundary conditions
• A Cartesian grid embedded boundary method for the heat equation and Poisson's equation in three dimensions
• A unified fictitious domain model for general embedded boundary conditions
• Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
• The immersed boundary method
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrande multiplier method
• Domaines fictifs, éléments finis H(div) et condition de Neumann: le problème de la condition inf-sup
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Discontinuous Galerkin Discretization with Embedded Boundary Conditions
• The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments
• Concept de zoom adaptatif en architecture multigrille locale ; étude comparative des méthodes L.D.C., F.A.C. et F.I.C.
• Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method
• A smoothness preserving fictitious domain method for elliptic boundary-value problems
• Methods of conjugate gradients for solving linear systems
• A Cartesian grid embedded boundary method for the heat equation on irregular domains