On the regular composite difference method for Laplace's equation on polygons

zbMath0398.65068MaRDI QIDQ1254101

Evgeny Volkov

Publication date: 1976

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Difference EquationsConvergence RateLaplace's EquationConvergence of the Approximate SolutionMixed Boundary- Value ProblemRegular Composite Difference MethodUniform Square Mesh 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Additive difference equations (39A10) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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On the solution of a nonlocal problem ⋮ A highly accurate difference method for solving the Dirichlet problem for Laplace’s equation on a rectangle ⋮ On the numerical solution of a multilevel nonlocal problem ⋮ Approximation on the hexagonal grid of the Dirichlet problem for Laplace's equation ⋮ A highly accurate difference method for approximating the solution and its first derivatives of the Dirichlet problem for Laplace's equation on a rectangle ⋮ An Efficient Finite Element Method with Exponential Mesh Refinement for the Solution of the Allen-Cahn Equation in Non-Convex Polygons ⋮ Approximate grid solution of a nonlocal boundary value problem for Laplace’s equation on a rectangle ⋮ A highly-accurate finite element method with exponentially compressed meshes for the solution of the Dirichlet problem of the generalized Helmholtz equation with corner singularities ⋮ On the high order convergence of the difference solution of Laplace’s equation in a rectangular parallelepiped

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