Both of these elements are certainly present in Marlowe's Dr Faustus.

The element of peripeteia in a drama—or, indeed, any other literary work—represents a turning point for the character, or a moment at which the direction of the narrative changes because of a change in the character's belief system or personal direction. In Greek tradition, the peripeteia usually comes alongside, or just before, the anagnorisis, or revelation. It is for this reason that I'd argue that Faustus's peripeteia comes in Act V—"let Faustus live in hell a thousand years" if he could only be saved—rather than in Act II, in which Faustus has his first regrets about what he is doing ("Why waverest thou?").

In Act V, Faustus finally recognizes what hell really has in store for him, and the magnitude of what he has done, but it is now too late for him to turn back. This represents a moment of both understanding and of a sudden, desperate need to change his mind. So, this is both the anagnorisis and the peripeteia. Look at Faustus's last soliloquy in Act V, Scene II, which marks the final hour of Faustus's life. Faustus here wants time to slow down for him and "make perpetual day" if only he can be spared what is coming to him, but he knows this is impossible—"The devil will come, and Faustus must be damned."

Doctor Faustus is one of the classic Renaissance era tragedies. It does indeed contain both peripeteia and anagnorisis.

Peripeteia is a reversal of circumstances, a turning point for a tragic hero. Think of Romeo and Juliet, where the lovers marry and everything seems wonderful—then Romeo kills Tybalt in a rage, causing the downward trajectory of the lovers' fortunes.

In Faustus, it is hard to determine an exact "turning point," but one might say the turning point is when Faustus refuses to repent. The Good Angel advises him to do so after Faustus and Mephistopheles have an argument, but Faustus refuses. He does this over and over again, until he is at the brink of death, by which it is too late to repent.

Anagnorisis is a dramatic revelation. At the end of the play, Faustus realizes just how bad of an idea making a deal with the devil is. He realizes what is in store for him once he is damned and how precious his soul is. But it truly is too late at that point, making this discovery tragic.

Peripeteia could be described as a "reversal of fortunes" or a "turning point in a story"; it is some undoing of the truth as it is known. Anagnorisis is best described as "discovery" or "revelation." Thus, a combination of the two might include such tragic events as betrayal.

Doctor Faustus depicts the classic "deal with the devil" storyline, with a well-learned scholar exchanging his soul for a demonic servant and access to magical conjurations. What separates Faustus from other tragic heros is that he makes this choice not out of necessity, or trickery, but with full cognition. Faustus is perfectly aware that he is trading his soul for a few fleeting years of earthly power, and will be eternally damned afterward. Faustus is also repeatedly warned against this bargain, encouraged to repent, or to call on God; yet he never does so, always arguing that "what's done is done" and there's no point in trying.

While this may be a matter of opinion, I think that peripeteia and anagnorisis appear in Act V. Faustus is in his final hours on earth, and it is only now, at the last minute, that the full magnitude of his choices begin to weigh upon his conscience. Suddenly he realizes how long "eternity" really is. Suddenly his demonic servants taunt and torment him and promise him endless pain. Suddenly he sees the face of an angry God. The discovery is that Faustus finally knows what is in store for him, and what it truly means, and how poor of a deal he has struck with Lucifer. The great reversal or turning point is that he really does care more about his soul and salvation than earthly pleasures, but it is only now, at the last minute, that it truly is too late.