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

Yes

The meaning, grammar, and spelling of "ausente" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation: Brazilian Portuguese features more open, melodic vowels and less reduction of unstressed syllables, whereas Continental Portuguese tends to heavily reduce or "swallow" unstressed vowels, making the word sound more closed or clipped.

Brazilian Portuguese

1. O aluno estava ausente da aula hoje. (The student was absent from class today.)
2. Você parece ausente quando está muito cansado. (You seem absent when you are very tired.)
3. O sistema registrou vários funcionários ausentes. (The system recorded several absent employees.)
4. Ela ficou ausente durante toda a reunião da equipe. (She was absent during the entire team meeting.)
5. Ele é um pai ausente na vida do filho. (He is an absent father in his son's life.)

Continental Portuguese

1. O aluno estava ausente da aula hoje. (The student was absent from class today.)
2. Tu pareces ausente quando estás muito cansado. (You seem absent when you are very tired.)
3. O sistema registou vários funcionários ausentes. (The system recorded several absent employees.)
4. Ela ficou ausente durante toda a reunião da equipa. (She was absent during the entire team meeting.)
5. Ele é um pai ausente na vida do filho. (He is an absent father in his son's life.)