Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
- Volume: 12, Issue: 2, page 173-202
- ISSN: 0764-583X
Access Full Article
topHow to cite
topWahlbin, 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
top- 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. 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. L. BERS, F. JOHN and M. SCHECHTER, Partial Differential Equations, Interscience, New York, 1964. Zbl0126.00207MR163043
- 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. P. G. CIARLET, Numerical Analysis of the Finite Element Method, Séminaire de Mathématiques supérieures, Presse de l'Université de Montréal, 1976. Zbl0363.65083MR495010
- 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. 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. 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. 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. Yu. P. KRASOVSKII, An investigation of the Green's function (in Russian), Uspehi Mat. Nauk., vol. 20, 1965, pp. 267-268.
- 11. J. NECAS, Les Méthodes directes en Théorie des Équations elliptiques, Masson, Paris, 1967. MR227584
- 12. J. A. NITSHE, L∞-convergence for Finite Element Approximation, 2. Conference on Finite Eléments, Rennes, France, May 12-14, 1975.
- 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. A. H. SCHATZ, An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms, Math. Comput., vol. 28, 1974, pp. 959-962. Zbl0321.65059MR373326
- 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. 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. R. SCOTT, Optimal L∞ Estimates for the Finite Element Method on Irregular Meshes, Math. Comput., vol. 30, 1976, pp. 681-697. Zbl0349.65060MR436617
- 18. E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N. J., 1970. Zbl0207.13501MR290095
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.