Blood flow through the heart is driven by a complex motion of the endocardial heart wall, where dilation or contraction results in filling and ejection. Boundary-driven flows of this type are inherently sensitive to conservation principles. Considering the finite element approach to the arbitrary Lagrangian-Eulerian (ALE) form of the Navier-Stokes equations, we present analysis addressing critical assumptions concerning conservation and numerical approximation which affect the accuracy and stability of ALE schemes for boundary-driven flows. Copyright (c) 2007 John Wiley & Sons, Ltd.