stubbornly
US /ˈstʌb.ɚn.li/
UK /ˈstʌb.ɚn.li/
1.
in a determined way, especially by refusing to change your mind or be persuaded, even when it would be more sensible to do so
:
•
He stubbornly refused to admit he was wrong.
•
The old door stubbornly resisted all attempts to open it.