Dishwasher with a water container for condensation drying and method for filling same

The dishwasher has a washing tank for accommodating to-be-washed items, and a water container standing in heat conductive contact with the washing tank. A filling device fills the water container with water, and the water container provides a condensation surface during a drying process (TG) of a washing process (SG). The filling device is designed such that the water container is filled over a time period (ZTG) of the drying process in multiple filling phases (FP1-FP3). The filling device is controllable by a program control device for controlling the washing process. An independent claim is also included for a method for implementing a washing process for cleaning to-be-washed items.