A Large Eddy Simulation turbulence (LES) algorithm has been developed for finite element-based computational fluid dynamics, using a hybrid continuous-discontinuous Galerkin scheme. The test case for this was a backward-facing step, which is a well-known example with published experimental results for validation. This dataset contains output data from the validation testcase as well as mesh files for grid generation of the associated test case. It also contains the GMSH geometry file for the problem, and the GMSH mesh file with the final adapted mesh.