See paper for full list of authors - 103 pages in total, author list starting page 87, 58 figures, 10 tables, submitted to EPJC. All figures and tables are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2014-11/ ; Measurements of the electroweak production of a $W$ boson in association with two jets at high dijet invariant mass are performed using $\sqrt{s} = 7$ and $8$ TeV proton-proton collision data produced by the Large Hadron Collider, corresponding respectively to 4.7 and 20.2 fb$^{-1}$ of integrated luminosity collected by the ATLAS detector. The measurements are sensitive to the production of a $W$ boson via a triple-gauge-boson vertex and include both the fiducial and differential cross sections of the electroweak process.