A method for the additive manufacture of a workpiece with the steps a. providing of a work table within the zone of influence of a set of radiation sources, wherein the set of radiation sources comprises at least one radiation source and wherein the work table comprises at least one lowerable lifting area in a starting position, b. providing of a layer of powdery raw material on the lifting area, c. exposing of regions of the first material layer which correspond to the desired shape of the workpiece to radiation from the radiation source so that the raw material in said regions is at least partially heated to at least its melting point, d. lowering of the lifting area with respect to the starting position, e. providing of a further layer of raw material on the layer which has been exposed before, f. exposing of regions of the further material layer which correspond to the desired shape of the workpiece to radiation from the radiation source so that the powder in said regions is at least partially heated to at least its melting point, g. repeating of the steps d. to f. until completion of the workpiece, wherein the lifting area at the time of completion of the workpiece is in an end position, h. cooling of the completed workpiece on the lifting area, i. removing of the workpiece from the lifting area, characterized by the additional steps - calculating of the dead volume within the construction volume which is not required for the manufacture of the workpiece, corresponding to the space between the starting position and the end position of the lifting area, - occupying of the construction volume with one or several filling elements so that at least a part of the dead volume is occupied and a construction volume which is not occupied by filling elements remains, wherein the lifting area has an outer shape which allows lowering of the lifting area relative to the filling elements through the construction volume from the starting position into the end position. a. providing of a work table within the zone of influence of a set of radiation sources, wherein the set of radiation sources comprises at least one radiation source and wherein the work table comprises at least one lowerable lifting area in a starting position, b. providing of a layer of powdery raw material on the lifting area, c. exposing of regions of the first material layer which correspond to the desired shape of the workpiece to radiation from the radiation source so that the raw material in said regions is at least partially heated to at least its melting point, d. lowering of the lifting area with respect to the starting position, e. providing of a further layer of raw material on the layer which has been exposed before, f. exposing of regions of the further material layer which correspond to the desired shape of the workpiece to radiation from the radiation source so that the powder in said regions is at least partially heated to at least its melting point, g. repeating of the steps d. to f. until completion of the workpiece, wherein the lifting area at the time of completion of the workpiece is in an end position, h. cooling of the completed workpiece on the lifting area, i. removing of the workpiece from the lifting area, - calculating of the dead volume within the construction volume which is not required for the manufacture of the workpiece, corresponding to the space between the starting position and the end position of the lifting area, - occupying of the construction volume with one or several filling elements so that at least a part of the dead volume is occupied and a construction volume which is not occupied by filling elements remains,