An improved non-traditional finite element formulation for solving three-dimensional elliptic interface problems

DOI10.1016/j.camwa.2016.11.035zbMath1368.65237OpenAlexW2561167852MaRDI QIDQ2398443

Liwei Shi, Songming Hou, Liqun Wang

Publication date: 16 August 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.11.035

zbMATH Keywords

elliptic equationmatrix coefficientjump conditionnon-traditional finite element methodthree-dimensional interface problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (12)

Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions ⋮ A stabilized coupled method and its optimal error estimates for elliptic interface problems ⋮ A Discontinuous Galerkin Method by Patch Reconstruction for Elliptic Interface Problem on Unfitted Mesh ⋮ A new Petrov-Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions ⋮ A three-dimensional Petrov-Galerkin finite element interface method for solving inhomogeneous anisotropic Maxwell's equations in irregular regions ⋮ A numerical method for solving elliptic interface problems using Petrov-Galerkin formulation with adaptive refinement ⋮ A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals ⋮ A simple weak formulation for solving two-dimensional diffusion equation with local reaction on the interface ⋮ A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions ⋮ A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients ⋮ Petrov-Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals ⋮ An Extremum-Preserving Iterative Procedure for the Imperfect Interface Problem

Uses Software

• IIMPACK

Cites Work

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• A numerical method for solving 3D elasticity equations with sharp-edged interfaces
• A weak formulation for solving elliptic interface problems without body fitted grid
• Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
• A numerical method for solving variable coefficient elliptic equation with interfaces
• An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity
• The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
• A sharp interface finite volume method for elliptic equations on Cartesian grids
• A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces
• Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
• Implicit second-order immersed boundary methods with boundary mass
• A three-dimensional computational method for blood flow in the heart. I: Immersed elastic fibers in a viscous incompressible fluid
• Numerical analysis of blood flow in the heart
• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• The immersed interface method using a finite element formulation
• The immersed finite volume element methods for the elliptic interface problems
• New Cartesian grid methods for interface problems using the finite element formulation
• An adaptive version of the immersed boundary method
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• A boundary condition capturing method for Poisson's equation on irregular domains
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• The finite element method for elliptic equations with discontinuous coefficients
• Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
• The extended finite element method for rigid particles in Stokes flow
• A Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem
• A discontinuous Galerkin method for elliptic interface problems with application to electroporation
• The immersed boundary method
• Three-dimensional immersed finite element methods for electric field simulation in composite materials
• An Extended Finite Element Method for Two-Phase Fluids
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• An unfitted finite element method using discontinuous Galerkin
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• A Numerical Method for Solving Elasticity Equations with Interfaces
• An immersed finite element space and its approximation capability
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• A Numerical Method for Solving the Elliptic Interface Problems with Multi-Domains and Triple Junction Points
• A finite element method for crack growth without remeshing
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• The Immersed Interface Method
• A boundary condition capturing method for multiphase incompressible flow.

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