Advection of material volumes in a three-dimensional cavity flow is analyzed by using an experimental setup and a collection of computational tools. The experimental setup for the lid-driven cavity flow makes it possible to study the advection of drops for a wide range of flow parameters. The location of unmixed regions for a specific mixing protocol is predicted by means of the mapping method, which are then used to determine the initial location of the dyed drops in the experiments. Finally, an adaptive front tracking method is used to computationally follow the drops during flow in a precise way. In most cases, a qualitative comparison between the experiments and the simulations is found. In addition, the mapping method proves to be well suited to quickly predict unmixed regions in mixers.