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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 3, Pages 503-509

Finite element estimates for a class of nonlinear variational inequalities

Mathematics Department, College of Science, P.O. Box 2455, King Saud University, Riyadh 11421, Saudi Arabia

Received 5 November 1990; Revised 16 March 1991

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that a wide class of obstacle and unilateral problems arising in pure and applied sciences can be studied in a general and unifield framework of variational inequalities. In this paper, we derive the error estimates for the finite element approximate solution for a class of highly nonlinear variational inequalities encountered in the field of elasticity and glaciology in terms of W1,p(Ω) and Lp(Ω)-norms. As a special case, we obtain the well-known error estimates for the corresponding linear obstacle problem and nonlinear problems.