Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems
Abstract: New high-order accurate finite difference schemes based on defect correction are considered for an initial boundary-value problem on an interval for singularly perturbed parabolic PDEs with convection; the highest space derivative in the equation is multiplied by the perturbation parameter ε. Solutions of the well-known classical numerical schemes for such problems do not converge ε-uniformly (the errors of such schemes depend on the value of the parameter ε and are comparable with the solution itself for small values of ε). The convergence order of the existing ε-uniformly convergent schemes does not exceed 1 in space and time. In this paper, using a defect correction technique, we construct a special difference scheme that converges ε-uniformly with the second (up to a logarithmic factor) order of accuracy with respect to x and with the second order of accuracy and higher with respect to t.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems ; volume:3 ; number:3 ; year:2003 ; pages:387-404
Computational methods in applied mathematics ; 3, Heft 3 (2003), 387-404
- Creator
-
Hemker, Pieter W.
Shishkin, Gregorii I.
Shishkin, Lidia P.
- DOI
-
10.2478/cmam-2003-0025
- URN
-
urn:nbn:de:101:1-2410261609346.332485044473
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
15.08.2025, 7:25 AM CEST
Data provider
This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Hemker, Pieter W.
- Shishkin, Gregorii I.
- Shishkin, Lidia P.
Other Objects (12)
High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
Long term behaviour of singularly perturbed parabolic degenerated equation
Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations
Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection–diffusion problems
Singularly perturbed differential equations
Uniformly convergent finite element methods for singularly perturbed convection diffusion equations
Singularly Perturbed Convection — Diffusion Problems in One Dimension: Bounds on Derivatives
High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
Long term behaviour of singularly perturbed parabolic degenerated equation
Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations
Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection–diffusion problems
Singularly perturbed differential equations
Uniformly convergent finite element methods for singularly perturbed convection diffusion equations
Singularly Perturbed Convection — Diffusion Problems in One Dimension: Bounds on Derivatives
High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions
Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers
Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes
Long term behaviour of singularly perturbed parabolic degenerated equation
Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations
Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data
A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection–diffusion problems
Singularly perturbed differential equations
Uniformly convergent finite element methods for singularly perturbed convection diffusion equations