Several well-known glacial landforms (such as U-shaped troughs and cirques) are associated with characteristic length scales, indicating that the viscosity of the ice and the stress gradients associated with ice flow exert first-order controls on their formation. The evolution of these glacial landforms has so far mostly been explored using phenomenological models that simply link the subglacial erosion rate to sliding or ice discharge. In order to improve our understanding of the causal links between the glacial landforms and the physics of the subglacial environment, we have performed computational experiments with a higher-order ice sheet model (Egholm et al., 2009) capable of simulating the long-term evolution of subglacial dynamics at a high spatial resolution. The orientation and magnitude of subglacial stress components depend not only on ice thickness and ice surface gradients, but also on the details of the bed topography and the regional variations in ice flow velocity. As glaciers erode their beds and modify the morphology of glaciated valleys, the subglacial dynamics therefore change with important implications for the sliding patterns and the continued erosion rates. We focus this presentation on feedbacks between the evolving bed topography and the subglacial erosion patterns. We have performed our experiments with different sliding and erosion laws, including highly non-linear rules representing coulomb-type slip at the bed (Schoof, 2010) and a quarrying model associated to the level of cavitation (Iverson, 2012). The highly non-linear computational experiments are made possible by new and very efficient GPU-accelerated multigrid algorithms. The computational experiments show that higher-order stress effects associated with local changes to the bed gradient provide important stabilizing effects for example in overdeepenings and near topographic steps. The experiments also show how a narrow and meandering pre-glacial valley represents a much more stable environment for a glacier than a glacially eroded valley where slip instabilities can readily propagate upstream.