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Approximation of an elliptic boundary value problem with unilateral constraints. (English) Zbl 0316.65024

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A15 Spline approximation
35J20 Variational methods for second-order elliptic equations
41A25 Rate of convergence, degree of approximation
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References:
[1] [1] BREZIS H. and STAMPACCHIA G., Sur La Régularité de La Solution d’Inéquations Elliptiques, Bulletin Soc. Math. France, vol. 96, 1968, pp. 153-180. Zbl0165.45601 MR239302 · Zbl 0165.45601 · numdam:BSMF_1968__96__153_0 · eudml:87105
[2] FALK R. S., Error Estimates for the Approximation of a Class of Variational Inequalities, Math. of Computation, vol. 28, 1974, pp. 963-971. Zbl0297.65061 MR391502 · Zbl 0297.65061 · doi:10.2307/2005358
[3] LEWY H. and STAMPACCHIA G., On the Regularity of the Solution of a Variational Inequality, Communications on Pure and Applied Mathematics, vol. 22, 1969, pp. 153-188. Zbl0167.11501 MR247551 · Zbl 0167.11501 · doi:10.1002/cpa.3160220203
[4] LIONS J. L. and STAMPACCHIA G., Variational Inequalities, Communications on Pure and Applied Mathematics, vol. 20, 1967, pp. 493-519. Zbl0152.34601 MR216344 · Zbl 0152.34601 · doi:10.1002/cpa.3160200302
[5] MOSCO U. and STRANG G., One-Sided Approximation and Variational Inequalities Bulletin Amer. math. Soc, vol.80, 1974, pp. 308-312. Zbl0278.35026 MR331818 · Zbl 0278.35026 · doi:10.1090/S0002-9904-1974-13477-4
[6] NITSCHE J., Lineare Spline-Funktionen und die Methoden vonRitz fur elliptische Randwertproblem, Archive for Rational Mechanics and Analysis, vol. 36, 1970, pp. 348-355. Zbl0192.44503 MR255043 · Zbl 0192.44503 · doi:10.1007/BF00282271
[7] NITSCHE J., Uber ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilraümen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg 36 (1970/71), pp.9-15. Zbl0229.65079 MR341903 · Zbl 0229.65079 · doi:10.1007/BF02995904
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