One external conflict is between Erik, the Phantom, and the new Opera directors. They believe the Phantom is nothing more than a legend, at worst a bad joke, and do not comply with any of the Phantom's rules, like leaving Box 5 empty for him and giving the starring lead to Christine. This conflict leads to many significant misfortunes like the chandelier (massive and candle-lit rather than electricity-lit) falling on the audience.
An internal conflict is the one that dramatizes the climax of the novel. Erik intends to blow up the Opera house and all its people if Christine accepts his proposal of marriage. The knobs that she must turn to indicate acceptance or rejection are rigged to lead one event or another. If Christine rejects him, the grasshopper knob he says she is to turn will ignite a whole basement-full of explosives. If she accepts him, the scorpion knob he says she is to turn will fill the basement with water, thus extinguishing the danger from the explosives.
The water rose in the cellar, above the barrels, the powder-barrels ... And we went up the stairs again in the dark, step by step, went up with the water.
Herein lies the internal conflict for Erik. Raol and the Persian, having been trapped in the basement with the explosives after escaping from the torture chamber, will drown as the water rapidly fills the under-chambers of the Opera after Christine has sacrificed her desire (an internal conflict for Christine) to save others from explosion by accepting Erik's proposal. The Phantom is going to let the two men drown despite their screams falling on his ears to save them. This internal conflict tearing at Erik's heart and mind is resolved when he relents in the face of Christine's love and saves them from drowning, an act anticlimactically referred to in an epilogue:
Erik returned with some little bottles which he placed on the mantelpiece. And, again in a whisper, so as not to wake M. de Chagny, he said to the Persian, after sitting down and feeling his pulse:
"You are now saved, both of you. And soon I shall take you up to the surface of the earth, TO PLEASE MY WIFE."