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

Yes

The word "novamente" is identical in meaning, spelling, and grammatical function (adverb) in both Brazilian and Continental Portuguese. The only differences are in pronunciation: Brazilian Portuguese typically features more open vowels and a more melodic, syllable-timed rhythm, whereas Continental Portuguese uses more closed vowels and a more stress-timed rhythm.

Brazilian Portuguese Examples

1. Eu preciso estudar novamente. (I need to study again.)
2. Ele falou novamente sobre o assunto. (He spoke about the subject again.)
3. Por favor, tente novamente. (Please, try again.)
4. Nós nos veremos novamente em breve. (We will see each other again soon.)
5. Ela começou novamente do zero. (She started again from scratch.)

Continental Portuguese Examples

1. Preciso estudar outra vez. (I need to study again.)
2. Ele voltou a falar do assunto. (He spoke about the subject again.)
3. Por favor, tenta de novo. (Please, try again.)
4. Ver-nos-emos outra vez em breve. (We will see each other again soon.)
5. Ela começou outra vez do zero. (She started again from scratch.)