Finite Element Methods for Mildly Nonlinear Elliptic Equations and Variational Inequalities

Whiteman, J. R.; Aslam Noor, M.

Whiteman, J. R. ; Aslam Noor, M.

Publications des séminaires de mathématiques et informatique de Rennes, Journées « éléments finis », no. S5 (1976), article no. 14, 12 p.

EuDML

@article{PSMIR_1976___S5_A14_0,
     author = {Whiteman, J. R. and Aslam Noor, M.},
     title = {Finite {Element} {Methods} for {Mildly} {Nonlinear} {Elliptic} {Equations} and {Variational} {Inequalities}},
     journal = {Publications des s\'eminaires de math\'ematiques et informatique de Rennes},
     eid = {14},
     pages = {1--12},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S5},
     year = {1976},
     language = {en},
     url = {http://www.numdam.org/item/PSMIR_1976___S5_A14_0/}
}

TY  - JOUR
AU  - Whiteman, J. R.
AU  - Aslam Noor, M.
TI  - Finite Element Methods for Mildly Nonlinear Elliptic Equations and Variational Inequalities
JO  - Publications des séminaires de mathématiques et informatique de Rennes
PY  - 1976
SP  - 1
EP  - 12
IS  - S5
PB  - Département de Mathématiques et Informatique, Université de Rennes
UR  - http://www.numdam.org/item/PSMIR_1976___S5_A14_0/
LA  - en
ID  - PSMIR_1976___S5_A14_0
ER  -

%0 Journal Article
%A Whiteman, J. R.
%A Aslam Noor, M.
%T Finite Element Methods for Mildly Nonlinear Elliptic Equations and Variational Inequalities
%J Publications des séminaires de mathématiques et informatique de Rennes
%D 1976
%P 1-12
%N S5
%I Département de Mathématiques et Informatique, Université de Rennes
%U http://www.numdam.org/item/PSMIR_1976___S5_A14_0/
%G en
%F PSMIR_1976___S5_A14_0

Whiteman, J. R.; Aslam Noor, M. Finite Element Methods for Mildly Nonlinear Elliptic Equations and Variational Inequalities. Publications des séminaires de mathématiques et informatique de Rennes, Journées « éléments finis », no. S5 (1976), article  no. 14, 12 p. http://www.numdam.org/item/PSMIR_1976___S5_A14_0/

Bibliographie
Cité par

1. Brezis H., and Stampacchia G., Sur la regularité de la solution d'inequations elliptiques. Bull. Soc. Math.France 96, 153-180, 1968. | Numdam | MR | Zbl

2. Ciarlet, P.G., and Raviart, P.A., General Lagrange and Hermite interpolation in R n with application to finite element methods. Arch. Rat. Mech. Anal. 46, 177-199, 1972. | MR | Zbl

3. Ciarlet, P.G., Schultz, M.H., and Varga, R.S., Numerical methods of high-order accuracy for nonlinear boundary value problems, I. One dimensional problems. Numer. Math. 9, 394-430, 1967. | MR | Zbl

4. Dailey, J.W., and Pierce, J.G., Error bounds for the Galerkin method applied to singular and nonsingular boundary value problems. Numer. Math. 19, 266-282, 1972. | MR | Zbl

5. Falk, R.S., Error estimates for the approximation of a class of variational inequalities. Math. Comp. 28, 963-971, 1974. | MR | Zbl

6. Fremond, M., Dual formulations for potential and complementary energies. Unilateral boundary conditions. Application to the finite element method, pp. 175-188 of J.R. Whiteman (ed.), The Mathematics of Finite Elements and Applications. Academic Press, London, 1973. | Zbl

7. Lions, J.L., and Stampacchia, G., Variational inequalities. Comm. Pure. Appl. Math. 20, 493-519, 1967. | MR | Zbl

8. Mosco, U., An introduction to the approximate solution of variational inequalities. In Constructive Aspects of Functional Analysis, Edizione Cremonese, Roma, 499-685, 1973. | Zbl

9. Mosco, U., and Strang, G., One sided approximation and variational inequalities. Bull. Amer. Math. Soc., 80, 308-312, 1974. | MR | Zbl

10. Natterer, F., Über die punktweise Konvergenz Finiter Elemente. Numer. Math. 25, 6-77, 1975. | MR | Zbl

11. Natterer, F., Optimal L2-Konvergenz Finiter Elemente bei Variationsungleichungen. I.S.N.M., Birkhäuser Verlag, Basel, (to appear). | MR | Zbl

12. Nitsche, J., Lineare Spline-Funktionen und die Methoden von Ritz fur elliptische Randwertprobleme. Arch. rat. Mech. Anal. 36, 348-355, 1970. | MR | Zbl

13. Nitsche, J., $L_{\infty}$ -convergence of finite element approximation. Journées Elements Finis, Rennes, May 1975. | MR | Zbl

14. Nitsche, J., $L_{\infty}$ -convergence of finite element approximations. Mathematical Aspect of the Finite Element Method. Rome, December 1975. | MR | Zbl

15. Noor, M.A., and Whiteman, J.R., Error bounds for finite element solutions of mildly nonlinear elliptic boundary value problems, (to appear in Numerische Mathematik, 1976). | MR | Zbl

16. Noor, M.A., and Whiteman, J.R., Error analysis of nonlinear variational inequalities, (to appear). | Zbl

17. Scott, R., Optimal $L_{\infty}$ estimates for the finite element method on irregular meshes (to appear). | MR | Zbl

18. Sibony, M., Approximation of nonlinear inequalities on Banach spaces, pp. 243-260 of A. Talbot (ed.) Approximation Theory. Academic Press, London, 243-260, 1970. | MR | Zbl

19. Stampacchia, G., Formes bilinéares coercitive sur les ensembles convexes, C.R.. Acad. Ac., Paris, 258, 4413-4416, 1964. | MR | Zbl

20. Strang, G., The finite element method - linear and nonlinear applications. International Congress of Mathematics, Vancouver. August, 1974. | MR | Zbl

21. Temam, R., Numerical Analysis. Reidel Publishing Co., Dordrecht, 1973. | MR | Zbl

22. Varga, R.S., Accurate numerical methods for nonlinear boundary value problems, pp. 152-167 of G.Birkhoff and R.S.Varga (eds.), Numerical Solution of Field Problems in Continuum Physics. American Mathematical Society, Providence, Rhode Island, 1970. | MR | Zbl

23. Whiteman, J.R., Some aspects of the Mathematics of finite elements in J.R. Whiteman (ed.), The Mathematics of Finite Elements and Applications II, MAFELAP 1975. Academic Press, London, to appear in 1976. | MR | Zbl