Some numerical experiments with multigrid methods on Shishkin meshes

DOI10.1016/S0377-0427(01)00365-XzbMath0994.65134OpenAlexW1967873831MaRDI QIDQ5957940

Francisco Javier Lisbona, Carmelo Clavero, Francisco José Gaspar

Publication date: 2 June 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(01)00365-x

zbMATH Keywords

convergencesingular perturbationnumerical experimentsconvection-diffusion problemsmultigrid methodShishkin mesh

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (7)

A Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion ⋮ Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Uniformly convergent additive schemes for 2D singularly perturbed parabolic systems of reaction-diffusion type ⋮ An analysis of diagonal and incomplete Cholesky preconditioners for singularly perturbed problems on layer-adapted meshes ⋮ A two-grid method for elliptic problem with boundary layers ⋮ Solving a Singularly Perturbed Elliptic Problem by a Multigrid Algorithm with Richardson Extrapolation

Uses Software

• Wesseling

Cites Work

• Fourier analysis of a robust multigrid method for convection-diffusion equations
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• A note on the conditioning of upwind schemes on Shishkin meshes
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