A direct method for accurate solution and gradient computations for elliptic interface problems

DOI10.1007/s11075-018-0503-5zbMath1412.65179OpenAlexW2791722132MaRDI QIDQ670478

Zhilin Li, Xiaohong Chen, Xiufang Feng

Publication date: 18 March 2019

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-018-0503-5

zbMATH Keywords

compact finite difference schemediscrete Green's functionconvergence proofelliptic interface problemaccurate solution and gradient computationdiscrete elliptic maximum principlevariable coefficient with discontinuities

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Boundary value problems for second-order elliptic equations (35J25) Finite difference methods for boundary value problems involving PDEs (65N06) Fictitious domain methods for boundary value problems involving PDEs (65N85)

Related Items (8)

A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients ⋮ A FFT accelerated fourth order finite difference method for solving three-dimensional elliptic interface problems ⋮ 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 ⋮ A stable RBF partition of unity local method for elliptic interface problems in two dimensions ⋮ Sixth order compact finite difference schemes for Poisson interface problems with singular sources ⋮ A Simple 3D Immersed Interface Method for Stokes Flow with Singular Forces on Staggered Grids ⋮ A second-order boundary condition capturing method for solving the elliptic interface problems on irregular domains

Uses Software

• IIMPACK

Cites Work

• A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions
• On the accuracy of finite difference methods for elliptic problems with interfaces.
• The method of difference potentials for the Helmholtz equation using compact high order schemes
• A boundary condition capturing method for Poisson's equation on irregular domains
• High-order difference potentials methods for 1D elliptic type models
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• A Fast Iterative Algorithm for Elliptic Interface Problems
• Numerical Solution of Partial Differential Equations
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients
• The Immersed Interface Method

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