Convergence of finite element approximation to quasilinear initial boundary value problems

Manfred Dobrowolski

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

  • Volume: 12, Issue: 3, page 247-266
  • ISSN: 0764-583X

How to cite

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Dobrowolski, Manfred. "Convergence of finite element approximation to quasilinear initial boundary value problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 12.3 (1978): 247-266. <http://eudml.org/doc/193322>.

@article{Dobrowolski1978,
author = {Dobrowolski, Manfred},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Quasilinear Partial Differential Equations; Congruence of Difference Methods; Error Estimates; Parabolic Initial Boundary Value Problem; Finite Element Method; Galerkin Approximation},
language = {eng},
number = {3},
pages = {247-266},
publisher = {Dunod},
title = {Convergence of finite element approximation to quasilinear initial boundary value problems},
url = {http://eudml.org/doc/193322},
volume = {12},
year = {1978},
}

TY - JOUR
AU - Dobrowolski, Manfred
TI - Convergence of finite element approximation to quasilinear initial boundary value problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1978
PB - Dunod
VL - 12
IS - 3
SP - 247
EP - 266
LA - eng
KW - Quasilinear Partial Differential Equations; Congruence of Difference Methods; Error Estimates; Parabolic Initial Boundary Value Problem; Finite Element Method; Galerkin Approximation
UR - http://eudml.org/doc/193322
ER -

References

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  1. 1. J H. BRAMBLE and S. R HILBERT, Bounds on a Class of Linear Functionals with Applications to Hermite Interpolation, Numer. Math., Vol 16, 1971, pp. 362-369 Zbl0214.41405MR290524
  2. 2. J H. BRAMBLE, A. W. SCHATZ, V. THOMEE and L. WAHLBIN, Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations, S.I.A M. J. Numer Anal , Vol. 14, 1977, pp 218-241. Zbl0364.65084MR448926
  3. 3 P. G. CIARLET and P A. RAVIART, General Lagrange and Hermite interpolation in R n with applications to finite element methods, Arch Rat.Mech Anal., Vol.46, 1972, pp 177-199 Zbl0243.41004MR336957
  4. 4. P. G. CIARLET and P A RAVIART, The Combined Effect of Curved Boundaries and Numerical Integration in the Isoparametnc Finite Element Method in The Mathematical Foundation of the Fmite Element Method with Applications to Partial Differential Equations, A. K. Aziz, Ed., Academic Press, New York, 1972 Zbl0262.65070MR421108
  5. 5 M DOBROWOLSKI, L -Fehlerabschatzungen in der Methode der finiten Elemente bei quasilinearen parabolischen Differential gleichungen zweiter Ordnung, Diplomarbeit No 13569, Bonn, 1976. 
  6. 6. J. Jr. DOUGLAS and T. DUPONT, Galerkin Methods for Parabohc Equations, S I.A M., J. Numer. Anal., Vol. 7, 1970, pp 575-626 Zbl0224.35048MR277126
  7. 7. J FREHSE, Optimale gleichmässige Konvergenz der Methode der finiten Elemente bei quasilinearen N -dimensionalen Randwertproblemen, Zeitschrift Angew. Math u. Mech., Tagungsband G.A M.M., 1976 (to appear). Zbl0357.65085MR436622
  8. 8. J. FREHSE and R. RANNACHER, Asymptotic L -error estimates for linear finite element approximations of quasilinear boundary value problems, S.I.A.M J Numer. Anal, (to appear). Zbl0386.65049MR502037
  9. 9 J. FREHSE and R RANNACHER, Optimal Uniform Convergence for the Finite Element Approximation of a Quasilinear Elliptic Boundary Value Problem, Preprint. Zbl0386.65049
  10. 10. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. L, 1964. Zbl0144.34903MR181836
  11. 11. O. A. LADYZENSKAJA, V A. SOLONNIKOV and N. N. URAL'CEVA, Linear and Quasihnear Equations of Parabolic Type, American Mathematical Society, Providence, Rhode Island, 1968 Zbl0174.15403
  12. 12. J. L. LIONS and E MAGENES, Problèmes aux limites non homogènes et applications, Vol. I, II. Dunod, Paris, 1968, 1970. Zbl0165.10801
  13. 13 J NITSCHE, L -Convergence of Finite Element Approximation, Preprint; 2. Conference on Finite Eléments, Rennes, 1975 Zbl0362.65088MR568857
  14. 14. R RANNACHER, Some Asymptotic Error Estimates for Finite Element Approximation of Minimal Surface , Preprint. Zbl0356.35034MR445866
  15. 15. V THOMÉE and L. WAHLBIN, On Galerkin Methods in Semilinear Parabolic Problems, Zbl0307.35007
  16. 16. M.F. WHEELER, A priori L 2 -Error Estimates for Galerkin Approximation to Parabohc Partial Differental Equations, S.I.A.M.J. Numer. Anal., Vol. 10, 1973, pp. 723-758. Zbl0232.35060MR351124
  17. 17 M. ZLÁMAL, Curved Elements in the Finite Element Methods, I S.I.A M., J Numer Anal., Vol. 10, 1973. pp. 229-249; II. S.I A.M, J. Numer Anal., Vol. 11, 1974, pp. 347-362 Zbl0285.65067MR343660

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