LAUSR

In this paper, we first formulate a linear quasi-static poroelastic shell model of Naghdi's type. The model is given in three unknowns: displacement u˜ of the middle surface, infinitesimal rotation ω˜ of the cross section of the shell, and the pressure π. The model has the structure of the quasi-static Biot's system and can be seen as a system of the shell equation with pressure term as forcing and the parabolic type equation for the pressure with divergence of the filtration velocity as forcing term. On the basis of the ideas of the operator splitting methods, we formulate two sequences of approximate solutions, corresponding to ‘undrained split’ and ‘fixed stress split’ methods. We show that these sequences converge to the solution of the poroelastic shell model. Therefore, the iterations constitute two numerical methods for the model. Moreover, both methods are optimized in a certain sense producing schemes with smallest contraction coefficient and thus faster convergence rates. Also, these convergences imply existence of solutions for the model. Copyright © 2017 John Wiley & Sons, Ltd.