On finite element approximation of general boundary value problems in nonlinear elasticity

Abstract

This paper deals with the approximate solution of the general boundary value problem in nonlinear elasticity by the finite element displacement method. Under usual conditions which also guarantee the existence of locally unique solutions the quasi-optimal convergence inL2 andL∞ is shown for displacement fields and stresses. Furthermore a projective Newton method is considered which reduces the solution of the nonlinear continuous problem to the successive solution of a sequence of linearized problems of increasing dimension. It is proved that this procedure is well defined and also converges with quasi-optimal rates.