Finite Element Methods for Mildly Nonlinear Elliptic Equations and Variational Inequalities

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

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

Publications mathématiques et informatique de Rennes no. S5 (1976), article no. 14, 12 p.

BibTeX
How to cite

@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 math\'ematiques et informatique de Rennes},
     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}
}

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

References

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 239302 | Zbl 0165.45601

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 336957 | Zbl 0243.41004

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 221761 | Zbl 0155.20403

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 301954 | Zbl 0244.65075

5. Falk, R.S., Error estimates for the approximation of a class of variational inequalities. Math. Comp. 28, 963-971, 1974. | MR 391502 | Zbl 0297.65061

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 0297.73062

7. Lions, J.L., and Stampacchia, G., Variational inequalities. Comm. Pure. Appl. Math. 20, 493-519, 1967. | MR 216344 | Zbl 0152.34601

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 0266.49005

9. Mosco, U., and Strang, G., One sided approximation and variational inequalities. Bull. Amer. Math. Soc., 80, 308-312, 1974. | MR 331818 | Zbl 0278.35026

10. Natterer, F., Über die punktweise Konvergenz Finiter Elemente. Numer. Math. 25, 6-77, 1975. | MR 474884 | Zbl 0331.65073

11. Natterer, F., Optimal L2-Konvergenz Finiter Elemente bei Variationsungleichungen. I.S.N.M., Birkhäuser Verlag, Basel, (to appear). | MR 451788 | Zbl 0358.65085

12. Nitsche, J., Lineare Spline-Funktionen und die Methoden von Ritz fur elliptische Randwertprobleme. Arch. rat. Mech. Anal. 36, 348-355, 1970. | MR 255043 | Zbl 0192.44503

13. Nitsche, J., $L_{\infty}$ -convergence of finite element approximation. Journées Elements Finis, Rennes, May 1975. | MR 568857 | Zbl 0362.65088

14. Nitsche, J., $L_{\infty}$ -convergence of finite element approximations. Mathematical Aspect of the Finite Element Method. Rome, December 1975. | MR 568857 | Zbl 0362.65088

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 438742 | Zbl 0312.65079

16. Noor, M.A., and Whiteman, J.R., Error analysis of nonlinear variational inequalities, (to appear). | Zbl 0521.65047

17. Scott, R., Optimal $L_{\infty}$ estimates for the finite element method on irregular meshes (to appear). | MR 436617 | Zbl 0349.65060

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 267334 | Zbl 0214.12501

19. Stampacchia, G., Formes bilinéares coercitive sur les ensembles convexes, C.R.. Acad. Ac., Paris, 258, 4413-4416, 1964. | MR 166591 | Zbl 0124.06401

20. Strang, G., The finite element method - linear and nonlinear applications. International Congress of Mathematics, Vancouver. August, 1974. | MR 423842 | Zbl 0334.65087

21. Temam, R., Numerical Analysis. Reidel Publishing Co., Dordrecht, 1973. | MR 347099 | Zbl 0261.65001

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 267748 | Zbl 0221.65130

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 455488 | Zbl 0351.65027