Dobrowolski, Manfred
Convergence of finite element approximation to quasilinear initial boundary value problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 12 (1978) no. 3 , p. 247-266
Zbl 0408.65067 | MR 509975
URL stable :


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 MR 290524 | Zbl 0214.41405

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. MR 448926 | Zbl 0364.65084

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 MR 336957 | Zbl 0243.41004

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 MR 421108 | Zbl 0262.65070

5 M Dobrowolski, L -Fehlerabschatzungen in der Methode der finiten Elemente bei quasilinearen parabolischen Differential gleichungen zweiter Ordnung, Diplomarbeit No 13569, Bonn, 1976.

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 MR 277126 | Zbl 0224.35048

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). MR 436622 | Zbl 0357.65085

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). MR 502037 | Zbl 0386.65049

9 J. Frehse and R Rannacher, Optimal Uniform Convergence for the Finite Element Approximation of a Quasilinear Elliptic Boundary Value Problem, Preprint.

10. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. L, 1964. MR 181836 | Zbl 0144.34903

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 Zbl 0174.15403

12. J. L. Lions and E Magenes, Problèmes aux limites non homogènes et applications, Vol. I, II. Dunod, Paris, 1968, 1970. Zbl 0165.10801

13 J Nitsche, L -Convergence of Finite Element Approximation, Preprint; 2. Conference on Finite Eléments, Rennes, 1975 MR 568857 | Zbl 0362.65088

14. R Rannacher, Some Asymptotic Error Estimates for Finite Element Approximation of Minimal Surface , Preprint. Numdam | MR 445866

15. V Thomée and L. Wahlbin, On Galerkin Methods in Semilinear Parabolic Problems, Zbl 0307.35007

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. MR 351124 | Zbl 0232.35060

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 MR 343660