An hp finite element method for convection-diffusion problems in one dimension

IMA Journal of Numerical Analysis

Volumn 19, Issue 3, 1999, Pages 425-453

  Melenk, Jens Markus ^a   Schwab, Christoph ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; FINITE ELEMENT METHOD; PIECEWISE LINEAR TECHNIQUES; TEST FACILITIES; VISCOSITY;

CONVECTION DIFFUSION PROBLEMS; CONVERGENCE ESTIMATES; EXPONENTIAL CONVERGENCE; HP-FINITE ELEMENT METHODS; LOCAL LEAST SQUARES; NUMERICAL EXPERIMENTS; NUMERICAL SOLUTION; TRANSPORT PROBLEMS;

HEAT CONVECTION;

EID: 0033245795     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/19.3.425     Document Type: Article

References (19)

1. CHRISTIE, J., GRIFFITHS, D. F., MITCHELL, A. R., & ZIENKIEWICZ, O. C. 1978 Finite element methods for second order differential equations with significant first derivatives. Int. J. Numer. Methods Eng. 10, 1764-1771.
2. DE GROEN, P. P. N. 1978 A finite element method with large mesh width for stiff two-point boundary value problems. Preprint, Department of Mathematics, Eindhoven University, Eindhoven, The Netherlands.
3. DE GROEN, P. P. N. & HEMKER, P. W. 1979 Error bounds for exponentially fitted Galerkin methods applied to stiff two-point boundary value problems. Numerical Analysis of Singular Perturbation Problems (P. W. Hemker and J. J. H. Miller, eds). New York: Academic.
4. GARTLAND, E. C. 1987 Uniform high-order difference schemes for a singularly perturbed two-point boundary value problem. Math. Comput. 48, 551-564.
5. HEMKER, P. W. 1977 A numerical study of stiff two-point boundary problems. PhD thesis, Mathematisch Centrum, Amsterdam.
6. HUGHES, T. J. & BROOKS, A. 1979 A multidimensional upwind scheme with no crosswind diffusion. Finite Element Methods for Convection Dominated Flows (AMD 34) (T. J. Hughes, ed). New York: American Society of Mechanical Engineers.
7. HUGHES, T. J. & BROOKS, A. 1982 A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions. Applications to the streamline diffusion procedure. Finite Elements in Fluids, vol. 4 (Gallagher, ed). New York: Wiley.
8. JOHNSON, C. & NÄVERT, U. 1981 An analysis of some finite element methods for advection-diffusion problems Analytical and Numerical Approaches to Asymptotic Problems in Analysis (O. Axelsson, L. S. Frank and A. van der Sluis, eds). Amsterdam: North-Holland, pp 99-116
9. KELLOGG, R. B. & TSAN, A. 1978 Analysis of some difference approximations for a singularly perturbed problem without turning points. Math. Comput. 32, 1025-1039.
10. MELENK, J. M. 1997 On the robust exponential convergence of finite element methods for problems with boundary layers. IMA J. Numer. Anal. 17, 577-601.
11. MELENK, J. M. & SCHWAB, C. 1997 An hp finite element method for convection-diffusion problems. Research Report 97-05, Seminar für Angewandte Mathematik, ETH Zürich. http://www.sam.math.ethz.ch/Reports/reports.html.
12. MELENK, J. M. & SCHWAB, C. 1998 The hp streamline-diffusion method for convection dominated problems in one space dimension. Research Report 98-10, Seminar für Angewandte Mathematik, ETH Zürich. http://www.sam.math.ethz.ch/Reports/reports.html.
13. MILLER, J. J. H, O'RIORDAN, E., & SHISHKIN, G. I. 1996 Fitted Numerical Methods for Singular Perturbation Problems. Singapore: World Scientific.
14. MORTON, K. W. 1995 Numerical Solution of Convection-Diffusion Problems. Oxford: Oxford University Press.
15. ROOS, H.-G., STYNES, M., & TOBISKA, L. 1996 Numerical Solution of Singularly Perturbed Boundary Value Problems. Heidelberg: Springer.
16. SCHWAB, C. & SURI, M. 1996 The p and hp versions of the finite element method for problems with boundary layers. Math. Comput. 65, 1403-1429.
17. SCHWAB, C., SURI, M., & XENOPHONTOS, C. A. 1996 Boundary layer approximation by spectral/ hp methods. Houston J. Math. Spec. Issue of ICOSAHOM '95 Conf. (A. V. Illin and L. R. Scott, eds), pp 501-508. (ISSN: 0362-1588).
18. SZYMCZAK, G. W. 1982 An adaptive finite element method for convection-diffusion problems. PhD Dissertation, University of Maryland, College Park.
19. SZYMCZAK, G. W. & BABUŠKA, I. 1984 Adaptivity and error estimation for the finite element method applied to convection diffusion problems. SIAM J. Numer. Anal. 21, 910-954.