Errors of finite element method for perfectly elasto-plastic problems. (English) Zbl 0856.73071

Repin, Sergey I.

Math. Models Methods Appl. Sci. 6, No. 5, 587-604 (1996).

This paper discusses convergence of the finite element method for variational problems of the Hencky plasticity theory. To obtain a priori convergence estimates, we use the method of “double approximation”. In the framework of this approach, perfectly elastoplastic problem is approximated by some regularized problem. Hence, finite element solutions of the regularized problem depend on the regularization parameter \(\delta\) and on the mesh parameter \(h\). We prove that there is a dependence between \(\delta\) and \(h\) such that piecewise-affine continuous approximations of the regularized problems generate a sequence of tensor valued functions which converges to the exact solution of the Hencky plasticity problem.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
74P10	Optimization of other properties in solid mechanics
74C99	Plastic materials, materials of stress-rate and internal-variable type

Keywords:

double approximation; convergence; variational problems; Hencky plasticity theory; regularized problem; regularization parameter; mesh parameter