How do Prospero and Ariel address each other?
When Prospero first addresses Ariel, he addresses Ariel as "servant" and is pretty brusque. Ariel calls Prospero "great master." There and in the following exchanges, Ariel is very subservient, responding immediately with great detail to Prospero's commands or need for information.
A bit later, though, Ariel gets restless. Ariel still sounds pretty respectful, but demands liberty, and Prospero has to be firmer, sliding over into abuse, calling Ariel "malignant thing." Ariel quiets down, and gives shorter answers, and the peace is restored. When Ariel misleads Ferdinand, Prospero praises Ariel, saying, "Thou hast done well, fine Ariel!"
Later, Ariel praises Ariel for Ariel's performance of the harpy, and compliments fly back and forth freely.
At the play's end, Prospero seems pretty affectionate, speaking of "my delicate Ariel."
They address each other informally using 'thee' instead of 'you' to portray their close relationship.