Abstract
Based on the nonlinear characters of the discrete problems of some elliptical variational inequalities, this paper presents a numerical iterative method, the schemes of which are pithy and converge rapidly. The new method possesses a high efficiency in solving such applied engineering problems as obstacle problems and free boundary problems arising in fluid lubrications.
Similar content being viewed by others
References
Glowinski, R.,Numerical Methods for Nonlinear Variational Problems. Springer Vering New York Inc. (1984).
Stuben, K., Algebraic multigrid (AMG): Experiences and comparisons,Appl. Math. Comput.,13 (1983), 419–451.
Zeng Jin-ping and Li Dong-hui, Convergence of multigrid iterative solutions for symmetric co-positive linear complimentary problems,Chinese Journal of Compt. Math., 1 (1994), 25–30 (in Chinese)
Lions, J. L. and G. Stampacchia, Variational Inequalities,Comm. Pure Appl. Math.,20 (1967), 493–519.
Kinderlenhrer, D. and G. Stanpacchia,An Introduction to Variational Inequalities and Their Applications, Acad. Press, New York (1980).
Zhou, S. Z., The error bound of finite element method for a two-dimensional singular boundary value problem.J. Comput. Math.,1 (1983), 143–147.
Cimatti, G., On a problem of the theory of lubrication governed by a variational inequalities,Appl. Math. Optim.,3, (1977), 227–242.
Zhou, S. Z., A direct method for the linear complimentary problem.J. Comput. Math.,8 (1990), 178–182.
Author information
Authors and Affiliations
Additional information
Communicated by He You-sheng
Project supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Tie-sheng, Z., Li, L. An iterative method for the discrete problems of a class of elliptical variational inequalities. Appl Math Mech 16, 351–358 (1995). https://doi.org/10.1007/BF02456948
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02456948