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**On a two-level Newton-type procedure applied for solving non-linear elasticity problems.**
*(English)*
Zbl 0994.74066

Summary: We apply the damped Newton method for solving a class of nonlinear elasticity problems. To this end, we consider a two-level procedure which involves (i) solving the nonlinear problem on a coarse mesh, (ii) interpolating the coarse-mesh solution to fine mesh, (iii) performing nonlinear iterations on the fine mesh. Numerical experiments suggest that in the case when one is interested in the minimization of the \(L_2\)-norm of the error rather than in the minimization of the residual norm, the coarse-mesh solution gives sufficiently accurate approximation to the displacement field on the fine mesh, and only a few (or even just one) of the costly nonlinear iterations on the fine mesh are needed to achieve an acceptable accuracy of the solution (the accuracy which is of the same order as the accuracy of Galerkin solution on the fine mesh).

### Keywords:

minimization of \(L(2)\) error norm; damped Newton method; nonlinear elasticity; two-level procedure; coarse mesh; fine mesh; nonlinear iterations
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\textit{O. Axelsson} and \textit{A. Padiy}, Int. J. Numer. Methods Eng. 49, No. 12, 1479--1493 (2000; Zbl 0994.74066)

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