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An upwind finite element method for singularly perturbed elliptic problems and local estimates in the L ∞ -norm

Uwe Risch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1990)

  • Volume: 24, Issue: 2, page 235-264
  • ISSN: 0764-583X

How to cite

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Risch, Uwe. "An upwind finite element method for singularly perturbed elliptic problems and local estimates in the $L^\infty $-norm." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.2 (1990): 235-264. <http://eudml.org/doc/193596>.

@article{Risch1990,
author = {Risch, Uwe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {cut-off-function-technique; hybrid upwind finite element method; singular perturbed 2-D elliptic problems; local estimates; boundary layers; three- direction grid; finite difference methods; order of convergence},
language = {eng},
number = {2},
pages = {235-264},
publisher = {Dunod},
title = {An upwind finite element method for singularly perturbed elliptic problems and local estimates in the $L^\infty $-norm},
url = {http://eudml.org/doc/193596},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Risch, Uwe
TI - An upwind finite element method for singularly perturbed elliptic problems and local estimates in the $L^\infty $-norm
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 2
SP - 235
EP - 264
LA - eng
KW - cut-off-function-technique; hybrid upwind finite element method; singular perturbed 2-D elliptic problems; local estimates; boundary layers; three- direction grid; finite difference methods; order of convergence
UR - http://eudml.org/doc/193596
ER -

References

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  1. [1] P. G. CIARLET, P. A. RAVIART, Maximum principle and uniforme convergence for the finite element method, Comp. Math. Appl. Mech. Engrg. 2 (1973) 17-31. Zbl0251.65069MR375802
  2. [2] T. IKEDA, Maximum principle in finite element models for convection-diffusion phenomena, North-Holland Publ. Comp., Amsterdam 1983. Zbl0508.65049MR683102
  3. [3] C. JOHNSON, A. H. SCHATZ, L. B. WAHLBIN, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp. 49 (1987), 25-38. Zbl0629.65111MR890252
  4. [4] U. NÄVERT, A finite element method for convection-diffusion problems, Thés., Göteborg 1982. 
  5. [5] K. OHMORI, T. USHIJIMA, A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations, R.A.I.R.O. Anal. Numer. 18 (1984) 3, 309-322. Zbl0586.65080MR751761
  6. [6] U. RISCH, Ein hybrides upwind-FEM-Verfahren und dessen Anwendung auf schwach gekoppelte elliptische Differentialgleichuungssysteme mit dominanter Konvektion, Thes., Magdeburg 1986. 
  7. [7] A. H. SCHATZ, L. B. WAHLBIN, On the FEM for singularly perturbed reaction diffusion problems in 2D and 1D, Math. Comp. 40 (1983), 47-89. Zbl0518.65080MR679434
  8. [8] M. TABATA, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ. 18 (1978), 327-351. Zbl0391.65038MR495024
  9. [9] L. TOBISKA, Diskretisierungsverfahren zur Lösung singulär gestörter Randwertprobleme, ZAMM 63 (1983), 115-123. Zbl0535.65058MR701842
  10. [10] H. YSERENTANT, Über die Maximumnormkonvergenz der Methode der finiten Elemente bei geringsten Regularitätsvoraussetzungen ZAMM 65 (1985) 2,91-100. Zbl0616.65103MR841262

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