×

Error estimates for the approximation of some unilateral problems. (English) Zbl 0358.65087


MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76B99 Incompressible inviscid fluids
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] 1. A. BERGER, R. SCOTT, G. STRANG, Approximate boundary conditions in the finite element method, Symposium on Numer. Anal. I.N.A.M. Roma. Symposia Mathematica Academic Press, 1973. Zbl0266.73050 MR403258 · Zbl 0266.73050
[2] 2. J. H. BRAMBLE, M. ZLAMAL, Triangular elements in the finite element method, Math.Comp., Vol. 24, 1970, pp. 809-820. Zbl0226.65073 MR282540 · Zbl 0226.65073
[3] 3. H. BREZIS, Problèmes unilatéraux, (Thèse), J. Math. Pures AppL, 1972. Zbl0237.35001 MR428137 · Zbl 0237.35001
[4] 4. R. W. COTTLE, R. S. SACHER, On the solution of large, structured linear complementarity problems : I, Tecn. Rep. 73-4 Stanford Univ. California.
[5] 5. R. W. COTTLE, G. H. GOLUB, R. S. SACHER, On the solution of large, structured linear complementarity problems: III, Tecn. Rep. 74-7 Stanford Univ. California.
[6] 6. R. W. COTTLE, Complementarity and variational problems, Tecn. Rep. 74-6 StanfordUniv. California.
[7] 7. R. W. COTTLE, Computational experience with large-scale linear complementarity problems, Tecn. Rep. 7-13 Stanford Univ. California.
[8] 8. G. DUVAUT, J. L. LIONS, Les inéquations en mécanique et en physique, Dunod, Paris, 1972. Zbl0298.73001 MR464857 · Zbl 0298.73001
[9] 9. R. S. FALK, Error estimates for the Approximation of a class of Variational Inequalities, Math, of Comp., Vol. 28, 1974, pp. 963-971. Zbl0297.65061 MR391502 · Zbl 0297.65061
[10] 10. M. FIEDLER, V. PTAK, On matrices with non-positive off-diagonal elements and positive principal minors, Czech. Math. J., Vol. 12, 1962, pp. 382-400. Zbl0131.24806 MR142565 · Zbl 0131.24806
[11] 11. R. GLOWINSKI, J. L. LIONS, R. TREMOLIERES, Book in print on the numerical analysis of the variational inequalities. Dunod, Paris. · Zbl 0508.65029
[12] 12. C. LEVATI, F. SCARPINI, G. VOLPI, Sul trattamento numerico di alcuni problemi variazionali di tipo unilaterale, L.A.N, del C.N.R., Vol. 82, 1974. Zbl0359.35001 · Zbl 0359.35001
[13] 13. J. L. LIONS, G. STAMPACCHIA, Variational inequalities, Comm. Pure Appl. Math.,Vol. 20, 1967, pp. 493-519. Zbl0152.34601 MR216344 · Zbl 0152.34601
[14] 14. J. L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Zbl0189.40603 MR259693 · Zbl 0189.40603
[15] 15. J. L. LIONS, E. MAGENES, Non-homogeneous boundary value problems and applications, I, II, III Springer., Berlin, 1972. Zbl0227.35001 · Zbl 0227.35001
[16] 16. U. Mosco, An introduction to the approximate solution of variational inequalities, Constructive Aspects of functional Analysis. Corso C.I.M.E. 1971 Cremonese Roma, 1973, Zbl0266.49005 · Zbl 0266.49005
[17] 17. U. Mosco, F. SCARPINI, Complementarity Systems and approximation of variational inequalities, R.A.I.R.O. R.l 1975, pp. 83-104. Zbl0338.49016 MR468153 · Zbl 0338.49016
[18] 18. U. Mosco, G. STRANG, One sided approximation and variational inequalities, Bull. A.M.S., Vol. 80, 1974, pp. 308-312. Zbl0278.35026 MR331818 · Zbl 0278.35026
[19] 19. U. Mosco, G. TROIANIELLO, On the smoothness of solutions of unilateral Dirichlet problems, Boll. U.M.I., Vol. 8, 1973, pp. 56-67. Zbl0277.35033 MR390479 · Zbl 0277.35033
[20] 20. J. NECAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967 . MR227584 · Zbl 1225.35003
[21] 21. R. S. SACHER, On the solution of large, structured linear complementarity problems: II, Teen. Rep. 73-5 Stanford Univ. California. Zbl0802.90106 · Zbl 0802.90106
[22] 22. F. SCARPINI, Some algorithms solving the unilatéral Dirichlet problem with two constraints. Calcolo, Vol. 12, 1975, pp. 113-149. Zbl0334.49004 MR426458 · Zbl 0334.49004
[23] 23. G. STAMPACCHIA, Variational inequalities, Theory and applications of monotone operators (Ghizzetti, A. ed.) Proceed. of NATO Advanced Study. Venice, 1968. Zbl0247.47050 MR425699 · Zbl 0247.47050
[24] 24. G. STRANG, A. E. BERGER, The change in solution due to change in domain, Proc. A.M.S. Symposium on partial differential equations. Berkeley, 1971. Zbl0259.35020 · Zbl 0259.35020
[25] 25. G. STRANG, Approximation in the finite element method, Numer. Math., Vol. 19, 1972, pp. 81-98. Zbl0221.65174 MR305547 · Zbl 0221.65174
[26] 26. G. STRANG, G. J. FIX, An analysis of the finite element method, Prentice-Hall, 1973. Zbl0356.65096 MR443377 · Zbl 0356.65096
[27] 27. F. TREVES, Topological vector spaces, distributions and kernels, Academic Press. New-York, 1967 . Zbl0171.10402 MR225131 · Zbl 0171.10402
[28] 28. M. M. VAINBERG, Variational methods for the study of nonlinear operators, Holden-Day, San Francisco, 1964. Zbl0122.35501 MR176364 · Zbl 0122.35501
[29] 29. M. ZLAMAL, Curved elements in the finite element method I, SIAM J. Numer. Anal. 10, 1973, 229-240 Zbl0285.65067 MR395263 · Zbl 0285.65067
[30] 30. M. ZLAMAL, Curved elements in the finite element method II, SIAM J. Numer.Anal. 11, 1974,347-362. Zbl0277.65064 MR343660 · Zbl 0277.65064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.