On the error estimate of finite difference method for the obstacle problem

Applied Mathematics and Computation

Volumn 183, Issue 1, 2006, Pages 416-422

  Cheng, Xiao liang ^a   Xue, Lian ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY CITY COLLEGE   (China)

Author keywords

Error estimates; Finite difference method; Maximum principle; Obstacle problem

Indexed keywords

FINITE DIFFERENCE METHOD; NUMERICAL METHODS; SET THEORY;

ERROR ESTIMATES; OBSTACLE PROBLEM;

ERROR ANALYSIS;

EID: 33845396747     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.05.082     Document Type: Article

References (14)

1. Duvaut G., and Lions J.-L. Inequalities in Mechanics and Physics (1976), Springer-Verlag, Berlin, Germany
2. Friedman A. Variational Principles and Free Boundary Problems (1982), John Wiley, New York
3. Glowinski R. Numerical Methods for Nonlinear Variational Problems (1984), Springer-Verlag, New York
4. Kikuchi N., and Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (1988), SIAM, Philadelphia, PA
5. Kinderlehrer D., and Stampacchia G. An Introduction to Variational Inequalities and Their Applications (1980), Academic Press, New York
6. Han W., and Reddy B.D. Plasticity: Mathematical Theory and Numerical Analysis (1999), Springer-Verlag, New York
7. Falk R.S. Error estimates for the approximation of a class of variational inequalities. Math. Comput. 28 (1974) 963-971
8. Wang L.H. Error estimates of two nonconforming finite elements for the obstacle problem. J. Comput. Math 4 (1986) 11-20
9. Wang L.H. On the error estimates of nonconforming finite element approximation to the obstacle problem. J. Comput. Math. 21 (2003) 481-490
10. Hafner K. Error estimates for the finite element solution of quasilinear obstacle problems. Numer. Funct. Anal. Optim. 9 (1987) 415-433
11. Liu W., Ma H., and Tang T. On mixed error estimates for elliptic obstacle problems. A posteriori error estimation and adaptive computational methods. Adv. Comput. Math. 15 (2001) 261-283
12. Chen Z.M., and Nochetto R.H. Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527-548
13. Kornhuber R. Monotone multigrid methods for elliptic variational inequalities I. Numer. Math 69 (1994) 167-184
14. Kornhuber R. Monotone multigrid methods for elliptic variational inequalities II. Numer. Math. 72 (1996) 481-499