Using simulations of a coarse-grained model, we examine the ability of topographic and chemical patterns to direct the self-assembly of thin films of copolymers into a defect-free array of vertical cylinders. The topographic pattern is a trench where the diblock is confined, whereas the chemical pattern consists of spots that interact preferentially with the minority block. The self-assembly process is described with Monte Carlo simulations of the standard model of block copolymers. While fully three-dimensional, the simulated systems can include over a hundred domains. By analyzing top views and cross sections of thin films, it is possible to determine the degree of ordering and the properties of individual domains. First, the influence of confinement on ordering perfection is examined. By focusing on the influence of trench width and sidewall selectivity, one can identify conditions that yield defect-free arrays with a high reliability and for which domains exhibit a high degree of uniformity across the trench. Second, we consider chemical patterns. While patterns matching the block copolymer morphology and characteristic dimensions yield defect-free self-assembly, we study the tolerance of directed self-assembly against deviations from this optimal case. We first explore the effect of a mismatch between the spacing of the pattern and the diblock characteristic dimensions, and then we examine the interpolation of domains on an incomplete pattern, where half of the rows are missing. By introducing placement error in the position of the spots, we assess to what extent the diblock can rectify the noise of a substrate pattern. The results of simulations are discussed in the context of a variety of experimental observations.