1 |
C.S. Ryoo, Numerical verification of solutions for Signorini problems using Newton-like mathod, International Journal for Numerical Methods in Engineering 73 (2008), 1181-1196.
DOI
|
2 |
G. Strang, G. Fix, An analysis of the finite element method, Englewood Cliffs, New Jersey, Prentice-Hall, 1973.
|
3 |
N.W. Bazley, D.W. Fox, Comparision operators for lower bounds to eigenvalues, J. reine angew. Math. 223 (1966), 142-149.
|
4 |
P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
|
5 |
U. Mosco, Approximation of the solutions of some variational inequalities, Roma: Press of Roma University, 1971.
|
6 |
J. Cea, Optimisation, theorie et algorithmes, Paris: Dunod, 1971.
|
7 |
X. Chen, A verification method for solutions of nonsmooth equations, Computing 58 (1997), 281-294.
DOI
|
8 |
R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer, New York, 1984.
|
9 |
I. Hlavacek, J. Haslinger, J. Necas, J. Lovisek, Solution of Variational Inequalities in Mechanics, Springer Ser. Appl. Math. Sci. 66 (1988), 221-265.
|
10 |
T. Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334-339.
DOI
|
11 |
N.J. Lehmann, Optimale Eigenwerteinschlieungen, Numer. Math. 5 (1963), 246-272.
DOI
|
12 |
M. Plum, Existence and Enclosure Results for Continua of Solutions of Parameter - Dependent Nonlinear Boundary Value Problems, Journal of Computational and Applied Mathematics 60 (1995), 187-200.
DOI
|
13 |
Y. Watanabe, N. Yamamoto, M.T. Nakao, Verified computations of solutions for nondifferential elliptic equations related to MHD equilibria. Nonlinear Analysis, Theory, Mathods & Applications 28 (1997), 577-587.
DOI
|
14 |
M. Plum, Explict H2-Estimates and Pointwise Bounds for Solutions of Second-Order Elliptic Bounday Value Problems. Journal of Mathematical Analysis and Appl. 165 (1992), 36-61.
DOI
|
15 |
M. Plum, Enclosures for weak solutions of nonlinear elliptic boundary value problems, WSSIAA, World Scientific Publishing Company 3 (1994), 505-521.
|
16 |
S.M. Rump, Solving algebraic problems with high accuracy, A new approach to scientific computation (Edited by U.W. KULISH and W.L. MIRANKER), Academic Press, New York, 1983.
|
17 |
C.S. Ryoo, Numerical verification of solutions for a simplified Signorini problem, Comput. Math. Appl. 40 (2000), 1003-1013.
DOI
|
18 |
C.S. Ryoo, An approach to the numerical verification of solutions for obstacle problems, Comput. Math. Appl. 53 (2007), 842-850.
DOI
|
19 |
C.S. Ryoo and R.P. Agarwal, Numerical inclusion methods of solutions for variational inequalities, International Journal for Numerical Methods in Engineering 54 (2002), 1535-1556.
DOI
|
20 |
C.S. Ryoo and R.P. Agarwal, Numerical verification of solutions for generalized obstacle problems, Neural, Parallel & Scientific Compuataions 11 (2003), 297-314.
|
21 |
C.S. Ryoo and M.T. Nakao, Numerical verification of solutions for variational inequalities, Numerische Mathematik 81 (1998), 305-320.
DOI
|
22 |
F. Scarpini, M.A. Vivaldi, Error estimates for the approximation of some unilateral problems, R.A.I.R.O. Numerical Analysis 11 (1977), 197-208.
|
23 |
F. Natterer, Optimale L2-Konvergenz finiter Elemente bei Variationsungleichungen, Bonn. Math. Schr. 89 (1976), 1-12.
|
24 |
M.T. Nakao, A numerical verification method for the existence of weak solutions for nonlinear boundary value problems, Journal of Math. Analysis and Appl. 164 (1992), 489-507.
DOI
|