On convergence of the immersed boundary method for elliptic interface problems

DOI10.1090/S0025-5718-2014-02932-3zbMath1311.65133OpenAlexW2110382229MaRDI QIDQ5179219

Zhilin Li

Publication date: 19 March 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02932-3

zbMATH Keywords

Dirac delta functionimmersed boundary (IB) methoddiscrete Green functiondiscrete Green's formulaconvergence of IB method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (12)

An immersed hybrid difference method for the elliptic interface equation ⋮ A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids ⋮ Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients ⋮ A shallow Ritz method for elliptic problems with singular sources ⋮ Sharp error estimates of a fourth‐order compact scheme for a Poisson interface problem ⋮ A modified equation analysis for immersed boundary methods based on volume penalization: applications to linear advection-diffusion equations and high-order discontinuous Galerkin schemes ⋮ Numerical integration rules with improved accuracy close to discontinuities ⋮ A simple augmented IIM for 3D incompressible two-phase Stokes flows with interfaces and singular forces ⋮ A high-order source removal finite element method for a class of elliptic interface problems ⋮ A Simple 3D Immersed Interface Method for Stokes Flow with Singular Forces on Staggered Grids ⋮ Analysis of the immersed boundary method for a finite element Stokes problem ⋮ Maximum error estimates of a MAC scheme for Stokes equations with Dirichlet boundary conditions

Uses Software

• FISHPAK
• IIMPACK

Cites Work

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• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• New Formulations for Interface Problems in Polar Coordinates
• On finite difference potentials and their applications in a discrete function theory
• On the Full C₁-Q_k Finite Element Spaces on Rectangles and Cuboids
• The Immersed Interface Method
• Discrete Interior Schauder Estimates for Elliptic Difference Operators

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