Gradient recovery for singularly perturbed boundary value problems II: Two-dimensional convection-diffusion

Mathematical Models and Methods in Applied Sciences

Volumn 11, Issue 7, 2001, Pages 1169-1179

  Roos, Hans Görg ^a   Linß, Torsten ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Convection diffusion problems; Finite element method; Gradient recovery; Shishkin type mesh; Singular perturbation; Superconvergence

Indexed keywords

EID: 18044400862     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202501001288     Document Type: Article

References (10)

1. M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. Engrg. 142 (1997) 1-88.
2. Eds. M. Křižek, P. Neittaanmäki and R. Stenberg, Finite Element Methods: Superconvergence, Post-Processing and a Posteriori Estimates (Marcel-Dekker, 1998).
3. T. Linß, Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem, IMA J. Numer. Anal. 20 (2000) 621-632.
4. T. Linß, Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes for a linear convection-diffusion problem, Numer. Methods Partial Differential Equations 16 (2000) 426-440.
5. T. Linß and M. Stynes, Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem, J. Math. Anal. Applic., to appear.
6. T. Linß and M. Stynes, Shishkin meshes for linear convection-diffusion problems, Comput. Methods Appl. Mech. Engrg. 190 (2001) 3527-3542.
7. H.-G. Roos and T. Linß, Sufficient conditions for uniform convergence on layer-adapted meshes, Computing 63 (1999) 27-45.
8. H.-G. Roos and T. Linß, Gradient recovery for singularly perturbed boundary value problems I: one-dimensional convection-diffusion, Computing 66 (2001) 163-178.
9. H.-G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Springer Series in Computational Mathematics, Vol. 24 (Springer, 1996).
10. O. C. Zienkiewicz and J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat J. Numer. Math. Engrg. 24 (1987) 337-357.