In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic
problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a
rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and
hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a duality algorithm are developed to cope with the convection dominating and nonlinear diffusion features,
respectively. Furthermore, in the duality method the convergence and optimal choice of the parameters are
analyzed. At each fixed point iteration, in the elastic model a complementarity formulation is required and appropriate numerical techniques are used. For the
spatial discretization different finite element spaces are chosen. Finally, numerical test examples illustrate the
theoretical results, as well as the good performance in the simulation of real devices.