Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem

IMA Journal of Numerical Analysis

Volumn 20, Issue 4, 2000, Pages 621-632

  Linss, Torsten ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; GALERKIN METHODS; HEAT CONVECTION; MESH GENERATION; NUMERICAL METHODS;

CONVECTION DIFFUSION PROBLEMS; GALERKIN FINITE ELEMENT METHODS; GLOBAL ENERGY; NUMERICAL EXPERIMENTS; PERTURBATION PARAMETERS; PIECEWISE UNIFORM MESH; SHISHKIN MESHES; SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0034347979     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/20.4.621     Document Type: Article

References (18)

1. APEL, TH. & DOBROWOLSKI, M. 1992 Anisotropic interpolation with applications to the finite element method. Computing 47, 277-293.
2. BAKHVALOV, N. S. 1969 Towards optimization of methods for solving boundary value problems in the presence of boundary layers. Zh. Vychisl. Mat. Mat. Fiz. 9, 841-859 (in Russian).
3. DOBROWOLSKI, M. & ROOS, H.-G. 1997 A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes. Z. Anal. Anwendungen 16, 1001-1012.
4. LINSS, T. 1999 An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem. J. Comput. Appl. Math. 110, 93-104.
5. LINSS, T. 2000 Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes. Numer. Methods Partial Differential Equation in press.
6. LINSS, T. & STYNES, M. 1999 A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems. Appl. Numer. Math. 31, 255-270.
7. LINSS, T. & STYNES, M. 2000a The SDFEM on Shishkin meshes for linear convection-diffusion problems. Numer. Math. in press.
8. LINSS, T. & STYNES, M. 2000b Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem. J. Math. Anal. Applic. in press.
9. MADDEN, N. & STYNES, M. 1997 Efficient generation of oriented meshes for solving convection-diffusion problems. Int. J. Numer. Methods Eng. 40, 565-576.
10. MILLER, J. J. H., O'RIORDAN, E., & SHISHKIN, G. I. 1996 Solution of Singularly Perturbed Problems with ∈-uniform Numerical Methods - Introduction to the Theory of Linear Problems in One and Two Dimensions. Singapore: World Scientific.
11. MORTON, K. W. 1996 Numerical Solution of Convection-Diffusion Problems (Applied Mathematics and Mathematical Computation 12). London: Chapman & Hall.
12. ROOS, H.-G. 1998 Layer-adapted grids for singular perturbation problems. Z. Angew. Math. Mech. 78, 291-309.
13. ROOS, H.-G. & LINSS, T. 1999 Sufficient conditions for uniform convergence on layer adapted grids. Computing 63, 27-45.
14. ROOS, H.-G., STYNES, M., & TOBISKA, L. 1996 Numerical Methods for Singularly Perturbed Differential Equations (Springer Series in Computational Mathematics 24). Berlin: Springer.
15. STYNES, M. & O'RIORDAN, E. 1997 A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem. J. Math. Anal. Applic. 214, 36-54.
16. STYNES, M. & TOBISKA, L. 1998a Analysis of the streamline-diffusion finite element method on a Shishkin mesh for a convection-diffusion problem with exponential layers. Preprint 17, Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg.
17. STYNES, M. & TOBISKA, L. 1998b A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Numer. Alg. 18, 337-360.
18. VULANOVIĆ, R. 2000 A priori meshes for singular perturbation problems. IMA J. Numer. Anal, in press.