We carried out large-scale atomistic molecular dynamics simulations to study the growth of twin lamellar crystals of polyethylene initiated by small crystal seeds. By examining the size distribution of the stems - straight crystalline polymer segments - we show that the crystal edge has a parabolic profile. At the growth front, there is a layer of stems too short to be stable, and new stable stems are formed within this layer, leading to crystal growth. Away from the edge, the lengthening of the stems is limited by a lack of available slack length in the chains. This frustration can be relieved by mobile crystal defects that allow topological relaxation by traversing through the crystal. The results shed light on the process of polymer crystal growth and help explain initial thickness selection and lamellar thickening.