The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems
From MaRDI portal
Publication:2021768
DOI10.1007/s11075-020-00964-zzbMath1471.65173OpenAlexW3036731176MaRDI QIDQ2021768
Thái Anh Nhan, Relja Vulanović
Publication date: 27 April 2021
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-020-00964-z
Diffusion (76R50) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06)
Related Items (13)
Analysis of a second-order hybrid scheme on Bakhvalov-type meshes: the truncation-error and barrier-function approach ⋮ A higher order hybrid-numerical approximation for a class of singularly perturbed two-dimensional convection-diffusion elliptic problem with non-smooth convection and source terms ⋮ Numerical solution of singularly perturbed 2-D convection-diffusion elliptic interface PDEs with Robin-type boundary conditions ⋮ Parameter uniform fitted mesh finite difference scheme for elliptical singularly perturbed problems with mixed shifts in two dimensions ⋮ Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions ⋮ Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type ⋮ A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layers ⋮ A finite difference method for a singularly perturbed 2‐D elliptic convection‐diffusion PDEs on Shishkin‐type meshes with non‐smooth convection and source terms ⋮ The robust numerical schemes for two-dimensional elliptical singularly perturbed problems with space shifts ⋮ Uniform convergence of finite element method on Bakhvalov-type triangular mesh for a singularly perturbed problem featuring exponential layers ⋮ Richardson extrapolation method for 2D-SPP on VB mesh singularly perturbed convection-diffusion problem on a Vulanović-Bakhvalov 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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some open questions in the numerical analysis of singularly perturbed differential equations
- An optimal a priori error estimate in the maximum norm for the Il'in scheme in 2D
- Robust convergence of a compact fourth-order finite difference scheme for reaction-diffusion problems
- Layer-adapted meshes for reaction-convection-diffusion problems
- A comparison of uniformly convergent difference schemes for two- dimensional convection diffusion problems
- The midpoint upwind scheme
- Layer-adapted meshes for convection-diffusion problems
- Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning
- A numerical method for stationary shock problems with monotonic solutions
- Preconditioning and uniform convergence for convection-diffusion problems discretized on Shishkin-type meshes
- A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
- An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
- A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems
- A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions
- The Capriciousness of Numerical Methods for Singular Perturbations
- Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
- Error Expansion for an Upwind Scheme Applied to a Two-Dimensional Convection-Diffusion Problem
- Estimating the error of numerical solutions of systems of reaction-diffusion equations
- Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
- Convection-Diffusion Problems
- A note on a generalized Shishkin-type mesh
- Analysis of the truncation error and barrier-function technique for a Bakhvalov-type mesh
- A parameter robust numerical method for a two dimensional reaction-diffusion problem
- A parameter‐robust numerical method for a system of reaction–diffusion equations in two dimensions
- The optimization of methods of solving boundary value problems with a boundary layer
- Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes
- Uniform convergence with respect to a small parameter of a scheme with central difference on refining grids
- Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
This page was built for publication: The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems
