International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 503-509
doi:10.1155/S0161171293000614
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 Muhammad Aslam Noor. 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.
Abstract
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.