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 suggeste d in earlier related publications, we consider a two-level procedure which involves (i) solving the non-linear problem on a coarse mesh, (ii) interpol ating the coarse-mesh solution to the line mesh, (iii) performing non-linea r iterations on the fine mesh. Numerical experiments suggest that in the ca se 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 soluti on gives sufficiently accurate approximation to the displacement field on t he fine mesh, and only a few (or even just one) of the costly non-linear it erations on the fine mesh are needed to achieve an acceptable accuracy of t he solution (the accuracy which is of the same order as the accuracy of the Galerkin solution on the fine mesh). Copyright (C) 2000 John Wiley C Sons, Ltd.