Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning

DOI10.1016/j.cam.2018.02.012zbMath1444.65041OpenAlexW2790683262MaRDI QIDQ1743962

Relja Vulanović, Martin Stynes, Thái Anh Nhan

Publication date: 16 April 2018

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

Full work available at URL: https://doi.org/10.1016/j.cam.2018.02.012

zbMATH Keywords

singular perturbationuniform convergencepreconditioningfinite differencesconvection-diffusionShishkin mesh

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (10)

An improved Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems ⋮ A Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion ⋮ Robust hybrid schemes of higher order for singularly perturbed convection-diffusion problems ⋮ Analysis of a second-order hybrid scheme on Bakhvalov-type meshes: the truncation-error and barrier-function approach ⋮ The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems ⋮ A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems ⋮ Analysis of the truncation error and barrier-function technique for a Bakhvalov-type mesh ⋮ A note on a generalized Shishkin-type mesh ⋮ A new upwind difference analysis of an exponentially graded Bakhvalov-type mesh for singularly perturbed elliptic convection-diffusion problems ⋮ A Uniform Convergence Analysis for a Bakhvalov-Type Mesh with an Explicitly Defined Transition Point

Cites Work

• Stability of a finite-difference discretization of a singular perturbation problem
• Layer-adapted meshes for reaction-convection-diffusion problems
• The midpoint upwind scheme
• Preconditioning and uniform convergence for convection-diffusion problems discretized on Shishkin-type meshes
• The uniform convergence with respect to a small parameter of A. A. Samarskij's monotone scheme and its modification
• Nonlinear singular perturbation phenomena: theory and applications
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
• A note on the conditioning of upwind schemes on Shishkin meshes
• A higher-order scheme for quasilinear boundary value problems with two small parameters
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning