A weak formulation for solving elliptic interface problems without body fitted grid

DOI10.1016/j.jcp.2013.04.025zbMath1314.65147OpenAlexW2006336694MaRDI QIDQ465561

Songming Hou, Peng Song, Liqun Wang, Hong-Kai Zhao

Publication date: 23 October 2014

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.04.025

zbMATH Keywords

finite element methodinterfaceelliptic equationsjump conditionnon-body fitted mesh

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Elliptic equations and elliptic systems (35J99)

Related Items (48)

Enriched gradient recovery for interface solutions of the Poisson-Boltzmann equation ⋮ A reconstruction-based Chebyshev-collocation method for the Poisson equation: an accurate treatment of the Gibbs-Wilbraham phenomenon on irregular interfaces ⋮ A fourth order finite difference method for solving elliptic interface problems with the FFT acceleration ⋮ A simple method for matrix-valued coefficient elliptic equations with sharp-edged interfaces ⋮ A Galerkin formulation of the MIB method for three dimensional elliptic interface problems ⋮ An improved non-traditional finite element formulation for solving three-dimensional elliptic interface problems ⋮ A numerical method for solving two-dimensional elliptic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition ⋮ Gradient preserved method for solving heat conduction equation with variable coefficients in double layers ⋮ Symmetric interior penalty Galerkin approaches for two-dimensional parabolic interface problems with low regularity solutions ⋮ A stabilized coupled method and its optimal error estimates for elliptic interface problems ⋮ An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems ⋮ A new weak Galerkin finite element method for elliptic interface problems ⋮ An interface-fitted mesh generator and virtual element methods for elliptic interface problems ⋮ Error analysis of Petrov-Galerkin immersed finite element methods ⋮ Shape optimization with immersed interface finite element method ⋮ Unfitted finite element methods for the heat conduction in composite media with contact resistance ⋮ Gradient recovery for elliptic interface problem. II: Immersed finite element methods ⋮ A numerical method for solving three-dimensional elliptic interface problems with triple junction points ⋮ A conforming enriched finite element method for elliptic interface problems ⋮ A Family of Immersed Finite Element Spaces and Applications to Three-Dimensional \(\bf{H}(\operatorname{curl})\) Interface Problems ⋮ A numerical method for solving elasticity equations with interface involving multi-domains and triple junction points ⋮ An immersed Crouzeix-Raviart finite element method in 2D and 3D based on discrete level set functions ⋮ A discrete fracture-matrix approach based on Petrov-Galerkin immersed finite element for fractured porous media flow on nonconforming mesh ⋮ Gradient recovery for elliptic interface problem. III: Nitsche's method ⋮ A finite volume method preserving maximum principle for the diffusion equations with imperfect interface ⋮ Numerical approximation based on immersed finite element method for elliptic interface optimal control problem ⋮ A numerical method for solving 3D elasticity equations with sharp-edged interfaces ⋮ An FE-FD Method for Anisotropic Elliptic Interface Problems ⋮ A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals ⋮ Imposing jump conditions on nonconforming interfaces for the correction function method: a least squares approach ⋮ A simple weak formulation for solving two-dimensional diffusion equation with local reaction on the interface ⋮ An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump ⋮ A Weak Formulation for Solving the Elliptic Interface Problems with Imperfect Contact ⋮ 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 ⋮ A Radial Basis Function Meshless Numerical Method for Solving Interface Problems in Irregular Domains ⋮ A high-order source removal finite element method for a class of elliptic interface problems ⋮ An Extremum-Preserving Iterative Procedure for the Imperfect Interface Problem ⋮ Numerical method for solving matrix coefficient elliptic equation on irregular domains with sharp-edged boundaries ⋮ Error estimates in weighted Sobolev norms for finite element immersed interface methods ⋮ Accurate gradient preserved method for solving heat conduction equations in double layers ⋮ A hybridizable discontinuous Galerkin method for elliptic interface problems in the formulation of boundary integral equations ⋮ Unfitted Nitsche's method for computing wave modes in topological materials ⋮ On the accuracy of finite element approximations to a class of interface problems ⋮ Higher-order finite element methods for elliptic problems with interfaces ⋮ An augmented matched interface and boundary (MIB) method for solving elliptic interface problem ⋮ Interface solutions of partial differential equations with point singularity ⋮ A new primal-dual weak Galerkin method for elliptic interface problems with low regularity assumptions

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• A new ghost cell/level set method for moving boundary problems: application to tumor growth
• A numerical method for solving variable coefficient elliptic equation with interfaces
• 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
• A second order virtual node method for elliptic problems with interfaces and irregular domains
• Improved volume conservation in the computation of flows with immersed elastic boundaries
• Numerical analysis of blood flow in the heart
• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• A level set approach for computing solutions to incompressible two-phase flow
• Finite element methods and their convergence for elliptic and parabolic interface problems
• New Cartesian grid methods for interface problems using the finite element formulation
• 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
• A coupling interface method for elliptic interface problems
• Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
• A kernel-free boundary integral method for elliptic boundary value problems
• 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 discontinuous Galerkin method for elliptic interface problems with application to electroporation
• 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
• Convergence of the ghost fluid method for elliptic equations with interfaces
• A Numerical Method for Solving Elasticity Equations with Interfaces
• A Boundary Condition--Capturing Multigrid Approach to Irregular Boundary Problems
• 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
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions
• The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
• The Immersed Interface Method

This page was built for publication: A weak formulation for solving elliptic interface problems without body fitted grid