A GENERALIZED NEWTON METHOD FOR HIGHER-ORDER FINITE ELEMENT APPROXIMATIONS IN NON-LINEAR ELASTICITY
P. PAPADOPOULOS and R. L. TAYLOR Int. J. Num. Meth. Engr., 39, pp. 2635-2646, (1996)

Abstract
A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.