Is the word divórcio the same in Brazilian and European Portuguese?

Yes

The word "divórcio" is identical in spelling, meaning, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, the pronunciation tends to be more open and musical (syllable-timed), whereas in Portugal, the vowels are more closed and the rhythm is more stress-timed, often making unstressed syllables sound much shorter or nearly swallowed.

Brazilian Portuguese examples:

1. O divórcio deles foi muito amigável. (Their divorce was very amicable.)
2. Ela está passando por um divórcio complicado. (She is going through a complicated divorce.)
3. O divórcio aconteceu de surpresa. (The divorce happened by surprise.)
4. Eles decidiram pelo divórcio após anos de crise. (They decided on divorce after years of crisis.)
5. O processo de divórcio está demorando muito. (The divorce process is taking a long time.)

Continental Portuguese examples:

1. O divórcio deles foi bastante pacífico. (Their divorce was quite peaceful.)
2. Ela está a passar por um divórcio complicado. (She is going through a complicated divorce.)
3. O divórcio ocorreu de forma inesperada. (The divorce occurred unexpectedly.)
4. Eles optaram pelo divórcio após anos de crise. (They opted for divorce after years of crisis.)
5. O processo de divórcio está a demorar muito. (The divorce process is taking a long time.)