On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

Han, Weimin; Reddy, B Daya

On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

Journal Article

1995

Journal Title

SIAM Journal on Numerical Analysis

Link to Journal

https://dx.doi.org/10.1137/0732081

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

We analyze the finite-element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed [B. D. Reddy, Nonlinear Anal., 19 (1992), pp. 1071-1089], and existence and uniqueness results for this problem have been given there. In this contribution the same approach is taken ; that is, finite-element approximations of the abstract variational inequality are analyzed, and the results are then discussed in further detail in the context of the concrete problems. Results on convergence are presented, as are error estimates. Regularization methods are commonly employed in variational inequalities of this kind, in both theoretical and computational investigations. We derive a posteriori error estimates which enable us to determine whether the solution of a regularized problem can be taken as a sufficiently accurate approximation of the solution of the original problem.

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