At least in conventional hydrostatic ice-sheet models, the numerical error associated with grounding line dynamics can be reduced by modifications to the discretization scheme. These involve altering the integration formulae for the basal traction and/or driving stress close to the grounding line and exhibit lower - if still first-order - error in the MISMIP3d experiments. MISMIP3d may not represent the variety of real ice streams, in that it lacks strong lateral stresses, and imposes a large basal traction at the grounding line. We study resolution sensitivity in the context of extreme forcing simulations of the entire Antarctic ice sheet, using the BISICLES adaptive mesh ice-sheet model with two schemes: the original treatment, and a scheme, which modifies the discretization of the basal traction. The second scheme does indeed improve accuracy - by around a factor of two - for a given mesh spacing, but km resolution is still necessary. For example, in coarser resolution simulations Thwaites Glacier retreats so slowly that other ice streams divert its trunk. In contrast, with km meshes, the same glacier retreats far more quickly and triggers the final phase of West Antarctic collapse a century before any such diversion can take place.