A method and a device for the continuous production of glass and glass ceramic products from a glass melt is provided, which simplifies the changing between two kinds of glass. The device includes a melting crucible and an induction coil, which preferably extends around the melting crucible in order to heat a glass melt by means of an induction field generated by the induction coil. The wall elements, which form the side wall of the crucible, have cooling channels, through which a cooling fluid can be conducted, so that the glass melt solidifies on the side wall and forms a skull layer. The interior side of the wall elements is formed at least in part by an aluminum nitride-containing ceramic.