The electronic states in a corner-overgrown bent GaAs/AlGaAs quantum well heterostructure are studied with numerical Hartree simulations. Transmission electron microscope pictures of the junction sharpness are shown to justify the sharp-corner potential assumed for these calculations. In a tilted magnetic field, both facets of the bent quantum well are brought to a quantum Hall (QH) state, and the corner hosts an unconventional hybrid system of coupled counter-propagating quantum Hall edges and an additional 1D accumulation wire. We show how, in contrast to coplanar barrier-junctions of QH systems, the coupling between the three subsystems increases as a function of the applied magnetic field, and discuss the implications of the numerical results for the interpretation of experimental data on bent quantum Hall systems reported elsewhere. DOI: 10.1103/PhysRevB.87.165428