Sixth order compact finite difference schemes for Poisson interface problems with singular sources

DOI10.1016/j.camwa.2021.07.020OpenAlexW3193899704MaRDI QIDQ2234865

Yanyan Li

Publication date: 19 October 2021

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

Full work available at URL: https://arxiv.org/abs/2104.07866

zbMATH Keywords

piecewise smooth solutionshigh order compact finite difference schemesdelta source functions Along curvesdiscontinuous and singular source termsPoisson interface equationsthe convergence proof

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (13)

A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients ⋮ A sixth order quasi-compact finite difference method for Helmholtz equations with variable wave numbers ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient ⋮ A FFT accelerated fourth order finite difference method for solving three-dimensional elliptic interface problems ⋮ Compact schemes in time with applications to partial differential equations ⋮ A compact sixth-order implicit immersed interface method to solve 2D Poisson equations with discontinuities ⋮ Sixth-order hybrid finite difference methods for elliptic interface problems with mixed boundary conditions ⋮ Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect ⋮ An adaptive support domain for the in-compressible fluid flow based on the localized radial basis function collocation method ⋮ Compact 9-point finite difference methods with high accuracy order and/or M-matrix property for elliptic cross-interface problems ⋮ A source term method for Poisson problems with a discontinuous diffusion coefficient ⋮ Nine-point compact sixth-order approximation for two-dimensional nonlinear elliptic partial differential equations: application to bi- and tri-harmonic boundary value problems ⋮ New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations

Uses Software

• IIMPACK

Cites Work

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