Polystyrene foamboard can be glued to concrete or to other foamboard panels with special low-volatile organic compound foamboard adhesive. If special foamboard adhesive is not available, general-use construction polystyrene adhesive can be used instead.
Low-VOC foamboard adhesive is sold in tubes that are intended to be used in a caulk gun. The adhesive sets up within minutes after exposure to the air. After gluing panels of foamboard to the wall, applying weatherproof tape over the seams can improve the insulating properties of the final result. Tape should also be applied to the edges where the foamboard meets the ceiling and floor.
Styrofoam insulation is more correctly called extruded polystyrene foamboard.