The highly accurate block-grid method in solving Laplace's equation for nonanalytic boundary condition with corner singularity

DOI10.1016/j.camwa.2011.12.068zbMath1252.65204OpenAlexW2070807418MaRDI QIDQ692300

M. C. Fu

Publication date: 4 December 2012

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.12.068

zbMATH Keywords

integral representationsingularityartificial boundaryblock-grid method9-point approximationflux intensity factors

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items

Numerical solution to Bitsadze-Samarskii type elliptic overdetermined multipoint NBVP ⋮ Approximation on the hexagonal grid of the Dirichlet problem for Laplace's equation ⋮ A method of harmonic extension for computing the generalized stress intensity factors for Laplace's equation with singularities ⋮ A highly accurate difference method for approximating the solution and its first derivatives of the Dirichlet problem for Laplace's equation on a rectangle ⋮ The block-grid method for the approximation of the pure second order derivatives for the solution of Laplace's equation on a staircase polygon ⋮ A fourth-order block-grid method for solving Laplace's equation on a staircase polygon with boundary functions in \(C^{k, \lambda}\) ⋮ Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions ⋮ One-block method for computing the generalized stress intensity factors for Laplace's equation on a square with a slit and on an L-shaped domain ⋮ Hexagonal grid approximation of the solution of the heat equation on special polygons

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Development of the block method for solving the Laplace equation for finite and infinite circular polygons
• Mesh independence of Newton-like methods for infinite dimensional problems
• Singularities and treatments of elliptic boundary value problems.
• A block-grid method of increased accuracy for solving Dirichlet's problem for Laplace's equation on polygons
• The block-grid method for solving Laplace's equation on polygons with nonanalytic boundary conditions
• AN EXPONENTIALLY CONVERGENT METHOD FOR THE SOLUTION OF LAPLACE'S EQUATION ON POLYGONS
• Computing flux intensity factors by a boundary method for elliptic equations with singularities
• Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
• A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities
• The High Accurate Block-Grid Method for Solving Laplace's Boundary Value Problem with Singularities
• A fourth order accurate difference-analytical method for solving Laplace’s boundary value problem with singularities
• A Singular Function Boundary Integral Method for Laplacian Problems with Boundary Singularities