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Error estimates for the approximation of a class of variational inequalities. (English) Zbl 0297.65061

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J20 Variational methods for second-order elliptic equations
41A15 Spline approximation
41A25 Rate of convergence, degree of approximation
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[1] Jean Pierre Aubin, Approximation of variational inequations, Functional Analysis and Optimization, Academic Press, New York, 1966, pp. 7 – 14.
[2] H. Brézis and M. Sibony, Équivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal. 41 (1971), 254 – 265 (French). · Zbl 0214.11104 · doi:10.1007/BF00250529 · doi.org
[3] Haïm R. Brezis and Guido Stampacchia, Sur la régularité de la solution d’inéquations elliptiques, Bull. Soc. Math. France 96 (1968), 153 – 180 (French). · Zbl 0165.45601
[4] R. S. FALK, Approximate Solutions of Some Variational Inequalities with Order of Convergence Estimates, Ph. D. Thesis, Cornell University, Ithaca, N. Y., 1971.
[5] Hans Lewy and Guido Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math. 22 (1969), 153 – 188. · Zbl 0167.11501 · doi:10.1002/cpa.3160220203 · doi.org
[6] J.-L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493 – 519. · Zbl 0152.34601 · doi:10.1002/cpa.3160200302 · doi.org
[7] Umberto Mosco, Approximation of the solutions of some variational inequalities, Ann. Scuola Norm. Sup. Pisa (3) 21 (1967), 373 – 394; erratum, ibid. (3) 21 (1967), 765. · Zbl 0184.36803
[8] Umberto Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances in Math. 3 (1969), 510 – 585. · Zbl 0192.49101 · doi:10.1016/0001-8708(69)90009-7 · doi.org
[9] J. Nitsche, Lineare Spline-Funktionen und die Methoden von Ritz für elliptische Randwertprobleme, Arch. Rational Mech. Anal. 36 (1970), 348 – 355 (German). · Zbl 0192.44503 · doi:10.1007/BF00282271 · doi.org
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