stubbornly
adverb /ˈstʌbənli/
  /ˈstʌbərnli/
 - (often disapproving) in a way that shows you are determined not to change your opinion or attitude synonym obstinately
- She stubbornly refused to pay.
 
 - in a way that is difficult to get rid of or deal with synonym persistently (2)
- Unemployment remains stubbornly high.