Error estimates for the approximation of a class of variational inequalities
HTML articles powered by AMS MathViewer
- by Richard S. Falk PDF
- Math. Comp. 28 (1974), 963-971 Request permission
Abstract:
In this paper, we prove a general approximation theorem useful in obtaining order of convergence estimates for the approximation of the solutions of a class of variational inequalities. The theorem is then applied to obtain an "optimal" rate of convergence for the approximation of a second-order elliptic problem with convex set $K = \{ \upsilon \in H_0^1(\Omega ):\upsilon \geqslant \chi$ a.e. in $\Omega$}.References
- Jean Pierre Aubin, Approximation of variational inequations, Functional Analysis and Optimization, Academic Press, New York, 1966, pp. 7–14. MR 0213889
- H. Brézis and M. Sibony, Équivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal. 41 (1971), 254–265 (French). MR 346345, DOI 10.1007/BF00250529
- Haïm R. Brezis and Guido Stampacchia, Sur la régularité de la solution d’inéquations elliptiques, Bull. Soc. Math. France 96 (1968), 153–180 (French). MR 239302 R. S. FALK, Approximate Solutions of Some Variational Inequalities with Order of Convergence Estimates, Ph. D. Thesis, Cornell University, Ithaca, N. Y., 1971.
- Hans Lewy and Guido Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math. 22 (1969), 153–188. MR 247551, DOI 10.1002/cpa.3160220203
- J.-L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493–519. MR 216344, DOI 10.1002/cpa.3160200302
- 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. MR 0226376
- Umberto Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances in Math. 3 (1969), 510–585. MR 298508, DOI 10.1016/0001-8708(69)90009-7
- J. Nitsche, Lineare Spline-Funktionen und die Methoden von Ritz für elliptische Randwertprobleme, Arch. Rational Mech. Anal. 36 (1970), 348–355 (German). MR 255043, DOI 10.1007/BF00282271
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 963-971
- MSC: Primary 65K05; Secondary 35J30
- DOI: https://doi.org/10.1090/S0025-5718-1974-0391502-8
- MathSciNet review: 0391502