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We compare global methods for solving models with jump discontinuities in the policy function. We find that differences between value function iteration (VFI) and other methods are economically significant and Euler equation errors fail to be a sufficient measure of accuracy in such models. VFI fails to accurately identify both the location and size of jump discontinuities, while the endogenous grid method (EGM) and the finite element method (FEM) are much better at approximating this class of models. We further show that combining VFI with a local interpolation step (VFI-INT) is sufficient to obtain accurate approximations. The combination of computational speed, relatively easy implementation and adaptability make VFI-INT especially suitable for approximating models with jump discontinuities in policy functions: while EGM is the fastest method, it is relatively complex to implement; implementation of VFI-INT is relatively straightforward and it is much faster than FEM.

In this paper, the fluid–structure interaction problem in mechanical systems in which a high frequency vibrating solid structure interacts with the surrounding fluid flow is considered. Such a situation normally appears in many microelectromechanical systems like a wide variety of microfluidic devices. A different implementation of the residual-based variational multiscale flow method is employed within the arbitrary Lagrangian–Eulerian formulation. The combination of the variational multiscale method with appropriate stabilization parameters is used to handle the so-called small time step instability in the finite element analysis of the fluid part in the coupled fluid–structure interaction problem. The capability of the employed approach has been demonstrated through finite element study of a benchmark example and FEM simulation of two different mechanical micropumping devices. High frequency vibrations of the solid membrane are used to derive the fluid flow in these micropumps. Results of FEM simulations are shown to be in good agreement with available experimental data. Copyright © 2012 John Wiley & Sons, Ltd.