On a two-level Newton-type procedure applied for solving non-linear elasticity problems

The present work is devoted to the damped Newton method applied for solving a class of non-linear elasticity problems. Following the approach suggested in earlier related publications, we consider a two-level procedure which involves (i) solving the non-linear problem on a coarse mesh, (ii) interpolating the coarse-mesh solution to the ne mesh, (iii) performing non-linear iterations on the ne mesh. Numerical experiments suggest that in the case when one is interested in the minimization of the L2-norm of the error rather than in the minimization of the residual norm the coarse-mesh solution gives su ciently accurate approximation to the displacement eld on the ne mesh, and only a few (or even just one) of the costly non-linear iterations on the ne mesh are needed to achieve an acceptable accuracy of the solution (the accuracy which is of the same order as the accuracy of the Galerkin solution on the ne mesh).