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

Yes

The word "jovem" is identical in meaning, spelling, and grammatical function in both Brazilian and European Portuguese. It can serve as both an adjective (meaning "young") and a noun (meaning "a young person" or "youth"). The only difference between the two dialects is pronunciation.

In Brazilian Portuguese, the final "e" is typically pronounced as a semi-vowel [i], and the "m" creates a strong nasalization that sounds almost like "jovim." In Continental (European) Portuguese, the unstressed "e" is much more closed and reduced, often sounding nearly silent or like a very short "u," and the "m" serves primarily to nasalize the preceding vowel, sounding more like "jov'n."

Brazilian Portuguese examples

1. Esse jovem é muito talentoso. (This young man is very talented.)
2. Eu me sinto jovem de espírito. (I feel young at heart.)
3. Os jovens de hoje em dia usam muita tecnologia. (Today's youth use a lot of technology.)
4. Ela é uma mulher jovem e cheia de energia. (She is a young woman full of energy.)
5. É importante ouvir o que os jovens têm a dizer. (It is important to listen to what young people have to say.)

European Portuguese examples

1. Esse rapaz é muito talentoso. (This boy/young man is very talented.)
2. Eu sinto-me jovem de espírito. (I feel young at heart.)
3. Os miúdos de hoje em dia usam muita tecnologia. (Kids/youngsters today use a lot of technology.)
4. Ela é uma mulher jovem e cheia de energia. (She is a young woman full of energy.)
5. É importante ouvir o que os jovens têm a dizer. (It is important to listen to what young people have to say.)