International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 755-766
On mixed finite element techniques for elliptic problems
Mathematics Department, King Saud University, P.O. Box 2455, Riyadh, Saudi Arabia
Received 6 February 1982; Revised 30 October 1982
Copyright © 1983 M. 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.
The main aim of this paper is to consider the numerical approximation of
mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.
It is shown that the saddle point, which minimizes the energy functional over the product space, is characterized by the variational equations. The eauivalence is used in deriving the error estimates for the finite element approximations. We give an example of a mildly nonlinear elliptic problem and show how the error estimates can be obtained from the general results.