The level‐set‐discrete‐element‐method (LS‐DEM) was developed to overcome the shape limitation of traditional discrete element method. LS‐DEM's shape generality relies on a node‐based surface discretization of grain boundary, and it has been used to shed new light of a variety of granular mechanics applications with realistically shaped grains and structural assemblies made of unbonded building blocks. Due to the node‐based discretization of grain boundary, the original LS‐DEM is discretization‐sensitive and it suffers from divergence of the response with discretization refinement, particularly for highly compressible problems. Previous studies have identified and addressed this issue in different ways, each with its own advantages and shortcomings. Here, we propose a methodologically‐rigorous and computationally‐efficient adapted formulation which solves LS‐DEM's discretization‐sensitivity issue. It adopts the classical contact description of continuum mechanics, wherein the contact interactions are traction‐based. We demonstrate the convergence of the adapted LS‐DEM in several highly compressible cases studies, show that it is key to correctly capturing the mechanical response, and compare it to alternative formulations.