SUMMARYA new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non-linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.

This paper presents an error estimator whichIn this paper, we present an error estimator based on the enables to control the quality of finite element solution in nonLadeveze's approach in 2D non-linear magnetostatic. Both linear magnetostatic. This method, based on the works of formulations in terms of scalar potential (cp-formulation) and P.Ladev6ze in mechanics, Consists in constructing a vector potential (A-formulation) are treated. To test the complementary admissible field from the one calculated by the proposed estimator, it is compared to the one based on the finite element method. This method has been transposed in the solution of both complementary problems on two examples, cases of non-linear vector and scalar potential 2D formulations. an iron core coil and a magnet with a magnetic circuit. The results given by the proposed estimator are compared to the one based on two finite element solutions on two examples. 11. ERROR IN CONSTITUTIVE RELATIONSHIP Let (H,B), called admissible couple, which verifies the Maxwell's equations and the boundary conditions on the domain D bounded by the surface S (S=S,uSb) :Index terms-error analysis, finite element methods, nonlinear systems, magnetostatics.

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