Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution

Applied Numerical Mathematics

Volumn 39, Issue 1, 2001, Pages 31-45

  Beckett, G ^a   Mackenzie, J A ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Adaptivity; Equidistribution; Finite element; Reaction diffusion; Singular perturbation; Uniform convergence

Indexed keywords

ERROR ANALYSIS; FINITE ELEMENT METHOD; PERTURBATION TECHNIQUES;

PERTURBED REACTION-DIFFUSION EQUATIONS;

BOUNDARY VALUE PROBLEMS;

EID: 0035479597     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(01)00049-6     Document Type: Article

References (27)

1. Optimal finite element solutions to diffusion-convection problems in one dimension
2. Convergence analysis of finite difference approximations on equidistributed grids to singularly perturbed boundary value problems
3. On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
4. On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
5. Grading functions and mesh redistribution
6. On the stability of mesh equidistribution strategies for time-dependent partial differential equations
7. Good approximation by splines with variables knots II
8. A high dimensional moving mesh strategy
9. Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements
10. Uniform pointwise convergence of finite difference schemes using grid equidistribution
11. Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid
12. On the robust exponential convergence of hp finite element methods for problems with boundary layers
13. A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction-diffusion problem
14. Mesh selection for discrete solution of boundary problems in ordinary differential equations
15. On the convergence of iterated remeshing
16. Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
17. Convergence analysis for an adaptive finite difference solution of a variable coefficient singular perturbation problem
18. Global uniformly convergent schemes for a singularly perturbed boundary value problem using patch base spline-functions
19. Adaptive mesh selection strategies for solving boundary value problems
20. The p and hp versions of the finite element method for problems with boundary layers
21. On selection of equidistributing meshes for two-point boundary problems