Summary
A thorough analysis of the finite element method is given for a holonomic elastic-plastic problem. An inequality of the Cea's lemma type is proved, which is the basis of error estimates for various finite element solutions. Difficulty caused by a non-differentiable term in the problem can be overcome by using two convergent procedures, an iterative procedure and a regularization procedure. An a-posteriori quantitative error estimate is derived for the regularized solution.
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The work was done while the author was at the Department of Mathematics, University of Maryland, College Park. The research was partially supported by the National Science Foundation grant CCR-88-20279
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Han, W. Finite element analysis of a holonomic elastic-plastic problem. Numer. Math. 60, 493–508 (1991). https://doi.org/10.1007/BF01385733
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DOI: https://doi.org/10.1007/BF01385733