Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration

L. B. Wahlbin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1978)

  • Volume: 12, Issue: 2, page 173-202
  • ISSN: 0764-583X

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Wahlbin, L. B.. "Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 12.2 (1978): 173-202. <http://eudml.org/doc/193318>.

@article{Wahlbin1978,
author = {Wahlbin, L. B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {2},
pages = {173-202},
publisher = {Dunod},
title = {Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration},
url = {http://eudml.org/doc/193318},
volume = {12},
year = {1978},
}

TY - JOUR
AU - Wahlbin, L. B.
TI - Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1978
PB - Dunod
VL - 12
IS - 2
SP - 173
EP - 202
LA - eng
UR - http://eudml.org/doc/193318
ER -

References

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  1. 1. S. AGMON, A. DOUGLIS and L. NIRENBERG, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. L, Comm. Pure Appl. Math., vol. 12, 1959, pp. 623-727. Zbl0093.10401MR125307
  2. 2. Yu. M. BEREZANSKH and Ya. A. ROITBERG, A Theorem on Homeomorphims and the Green's Function for General Elliptic Boundary Problems (in Russian), Ukrain. Math. Z., vol. 19, 1967, pp. 3-32 (English translation, Ukrain. Math. J., vol. 19, 1967, pp. 509-530). Zbl0206.11302MR218739
  3. 3. L. BERS, F. JOHN and M. SCHECHTER, Partial Differential Equations, Interscience, New York, 1964. Zbl0126.00207MR163043
  4. 4. J. H. BRAMBLE and S. HILBERT, Bounds for a Class of Linear Functionals with Applications to Hermite Interpolation, Numer. Math., vol. 16, 1971, pp. 362-369. Zbl0214.41405MR290524
  5. 5. P. G. CIARLET, Numerical Analysis of the Finite Element Method, Séminaire de Mathématiques supérieures, Presse de l'Université de Montréal, 1976. Zbl0363.65083MR495010
  6. 6. P. G. CIARLET and P.-A. RAVIART, General Lagrange and Hermite Interpolation in Rn with Applications to Finite Element Methods, Arch. Rat. Mech. Anal., vol. 46, 1972, pp. 177-199. Zbl0243.41004MR336957
  7. 7. P. G. CIARLET and P.-A. RAVIART, Interpolation Theory Over Curved Elements, with Applications to Finite Element Methods, Comput. Methods Appl. Mech.Engrg., vol. 1, 1972, pp. 217-249. Zbl0261.65079MR375801
  8. 8. P. G. CIARLET and P.-A. RAVIART, The Combined Effect of Curved Boundaries and Numerical Integration in Isoparametric Finite Element Methods, The Mathematical Foundations of the Finite Element Method, A. K. Aziz, Ed., Academic Press, New York, 1973, pp. 409-474. Zbl0262.65070MR421108
  9. 9. G. J. Fix, Effects of Quadrature Errors in Finite Element Approximation of Steady State, Eigenvalue and Parabolic Problems, The Mathematical Foundation of the Finite Element Method, A.K. Aziz, Ed., Academic Press, New York, 1973, pp. 525-556. Zbl0282.65081MR413546
  10. 10. Yu. P. KRASOVSKII, An investigation of the Green's function (in Russian), Uspehi Mat. Nauk., vol. 20, 1965, pp. 267-268. 
  11. 11. J. NECAS, Les Méthodes directes en Théorie des Équations elliptiques, Masson, Paris, 1967. MR227584
  12. 12. J. A. NITSHE, L∞-convergence for Finite Element Approximation, 2. Conference on Finite Eléments, Rennes, France, May 12-14, 1975. 
  13. 13. J. A. NITSCHE and A. H. SCHATZ, Interior Estimates for Ritz-Galerkin Methods, Math. Comput., vol. 28, 1974, pp. 937-958. Zbl0298.65071MR373325
  14. 14. A. H. SCHATZ, An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms, Math. Comput., vol. 28, 1974, pp. 959-962. Zbl0321.65059MR373326
  15. 15. A. H. SCHATZ and L. B. WAHLBIN, Interior Maximum Norm Estimates for Finite Element Methods, Math. Comput., vol 31, 1977, pp. 414-442. Zbl0364.65083MR431753
  16. 16. A. H. SCHATZ and L. B. WAHLBIN, Maximum Norm Estimates in the Finite Element Method on Plane Polygonal domains, Parti, Math. Comput. (to appear). Zbl0382.65058
  17. 17. R. SCOTT, Optimal L∞ Estimates for the Finite Element Method on Irregular Meshes, Math. Comput., vol. 30, 1976, pp. 681-697. Zbl0349.65060MR436617
  18. 18. E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N. J., 1970. Zbl0207.13501MR290095

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