The invention relates to the production of a glass melt (9) in a row arrangement, comprising at least one loading opening (7) for raw glass materials, a melting region (2), a refining region (3), a constriction (4), a conditioning region (5) and an overflow (8) into a processing unit. In order to remove flaws from the melt that remain visible in the end product, the invention proposes: a) arranging a refining bench (19) between the melting region (2) and the beginning of the refining region (3); b) arranging side burners (15, 17) and extraction openings (16, 18) for flue gases between the loading opening (7) and the refining bench (19); c) delimiting the constriction (4) at both ends by end walls (12, 13) that leave narrow flow cross-sections above the glass melt (9) for flue gases; and d) arranging cooling means for the glass melt (9) inside the constriction (4). The invention is particularly suited for producing flat glass and panels for solar elements. To this end, the oxidants for the fuels may also be preheated.