Satellite radar interferometry data reveals that the grounding line of Petermann Glacier, Greenland migrates by several kilometers during the tidal cycle, bringing pressurized, subsurface, warm ocean waters in regular contact with a large sector of grounded ice. We use the Massachusetts Institute of Technology general circulation model in two dimensions to calculate the ice melt rates as a function of grounding zone width and ocean thermal forcing. Ice melt rates are found to be higher in the grounding zone cavity than anywhere else in the ice shelf cavity. The melt rates increase sub-linearly with the width of the grounding zone and ocean thermal forcing. The model results agree well with remote sensing estimates of ice melt. High basal ice melt rates in tidally-flushed grounding zones imply that marine-terminating glaciers are more sensitive to ocean thermal forcing than anticipated, which will increase their projected contribution to sea level rise.