A numerical scheme based on mean value solutions for the Helmholtz equation on triangular grids

DOI10.1090/S0025-5718-97-00825-9zbMath0865.65074MaRDI QIDQ3127315

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Publication date: 8 April 1997

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

zbMATH Keywords

numerical examplesconvection-diffusion problemserror estimateDirichlet boundary value problemHelmholtz equationstruncated series approximationnon-standard difference approximation

Mathematics Subject Classification ID

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

Related Items (5)

Viscous Equations Treated with $$\mathcal{L}$$ -Splines and Steklov-Poincaré Operator in Two Dimensions ⋮ Dirichlet-to-Neumann mappings and finite-differences for anisotropic diffusion ⋮ Reprint of: ``Dirichlet-to-Neumann mappings and finite-differences for anisotropic diffusion ⋮ Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids ⋮ On mean value solutions for the Helmholtz equation on square grids

Cites Work

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• Single cell high order difference methods for the Helmholtz equation
• Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems. II: Convergence theory
• The numerical solution of the Dirichlet problem for the Helmholtz equation
• A single cell high order scheme for the convection-diffusion equation with variable coefficients
• High-order difference schemes for two-dimensional elliptic equations
• Discrete Weighted Mean Approximation of a Model Convection-Diffusion Equation
• Optimal Few-Point Discretizations of Linear Source Problems

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