An FE-FD Method for Anisotropic Elliptic Interface Problems

DOI10.1137/19M1291030zbMath1452.65332OpenAlexW3048485169MaRDI QIDQ5132028

Baiying Dong, Xiufang Feng, Zhilin Li

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1291030

zbMATH Keywords

finite element methodfinite difference methoderror analysisscaling techniquemaximum principle preserving schemeanisotropic elliptic interface problemnormal derivative computation

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (9)

A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients ⋮ A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients ⋮ An exact-interface-fitted mesh generator and linearity-preserving finite volume scheme for anisotropic elliptic interface problems ⋮ An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems ⋮ A robust, interpolation‐free and monotone finite volume scheme for diffusion equations on arbitrary quadrilateral meshes ⋮ Sixth-order hybrid finite difference methods for elliptic interface problems with mixed boundary conditions ⋮ Compact 9-point finite difference methods with high accuracy order and/or M-matrix property for elliptic cross-interface problems ⋮ Numerical Solutions of the Electromagnetic Scattering by Overfilled Cavities with Inhomogeneous Anisotropic Media ⋮ Sixth order compact finite difference schemes for Poisson interface problems with singular sources

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A weak formulation for solving elliptic interface problems without body fitted grid
• Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
• Sparse second moment analysis for elliptic problems in stochastic domains
• A robust numerical method for the random interface grating problem via shape calculus, weak Galerkin method, and low-rank approximation
• A numerical method for solving elliptic interface problems using Petrov-Galerkin formulation with adaptive refinement
• Phase field approach with anisotropic interface energy and interface stresses: large strain formulation
• How to obtain an accurate gradient for interface problems?
• A kernel-free boundary integral method for elliptic boundary value problems
• The finite element method for elliptic equations with discontinuous coefficients
• Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• Level-set function approach to an inverse interface problem
• Singularities, interfaces and cracks in dissimilar anisotropic media
• Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
• An Immersed Interface Method for Solving Anisotropic Elliptic Boundary Value Problems in Three Dimensions
• Inf‐sup stability of Petrov‐Galerkin immersed finite element methods for one‐dimensional elliptic interface problems
• Numerical Solution of Partial Differential Equations
• An immersed interface method for anisotropic elliptic problems on irregular domains in 2D
• A partially penalty immersed interface finite element method for anisotropic elliptic interface problems
• First order second moment analysis for stochastic interface problems based on low-rank approximation
• Finite Elements

This page was built for publication: An FE-FD Method for Anisotropic Elliptic Interface Problems