Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems

Applied Numerical Mathematics

Volumn 38, Issue 3, 2001, Pages 315-345

  Liu, Wenbin ^a   Tang, Tao ^b  

^a UNIVERSITY OF KENT   (United Kingdom)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Boundary layer; Error estimates; Spectral methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; GALERKIN METHODS; MATHEMATICAL TRANSFORMATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

GALERKIN-SPECTRAL METHOD;

ERROR ANALYSIS;

EID: 0035425658     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(01)00036-8     Document Type: Article

References (29)

1. Properties of some weighted Sobolev spaces and applications to spectral approximations
2. Chebyshev and fourier spectral methods
3. Spectral methods and a maximum principle
4. Spectral methods in fluid dynamics
5. A deferred correction method for nonlinear two-point boundary value problems
6. A new method of stabilization for singular perturbation problems with spectral methods
7. Spectral integration and two-point boundary value problem
8. A new pseudospectral method with upwind features
9. On the use of nonlinear grids in finite-difference equations
10. Analysis of some difference approximations for a singular perturbation problem without turning points
11. Numerical methods for stiff two-point boundary value problems
12. A fast adaptive numerical method for stiff two-point boundary value problems
13. An adaptive finite difference solver for nonlinear two-point boundary problems with mild boundary layers
14. A new efficient spectral Galerkin methods for singular perturbation problems
15. A new boundary layer resolving spectral method
16. An efficient algorithm for solving general linear two point BVP
17. Pseudospectral solutions of near-singular problems using numerical coordinate transformations based on adaptivity
18. Numerical simulation of viscous incompressible flows
19. On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions
20. The p and hp versions of the finite element method for problems with boundary layers
21. Efficient spectral-Galerkin method I: Direct solvers for the Helmholtz equation and the biharmonic equation using Legendre polynomials
22. Efficient spectral-Galerkin method II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials
23. A finite element method for a singularly perturbed boundary value problem
24. Boundary layer resolving pseudospectral method for singular perturbation problems