to insist
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to insist on
To persist stubbornly and unyieldingly in an opinion, position, or demand.
Er beharrte auf seiner Meinung, obwohl alle anderen anderer Ansicht waren.
He insisted on his opinion, although everyone else had a different view.
'Beharren' (to insist) is an inseparable verb. The prefix 'be-' remains firmly attached to the verb stem 'harren' in all tenses and sentence constructions.
Sie beharrte darauf, die Rechnung sofort zu bezahlen.
She insisted on paying the bill immediately.
In the meaning 'auf etwas bestehen' (to insist on something), 'beharren' (to insist) is almost always used with the preposition 'auf' and the dative. You insist on something.
Der Anwalt beharrte auf dem Recht seines Mandanten.
The lawyer insisted on his client's right.
People typically 'beharren' (insist) on abstract things such as an opinion, a position, a right, a demand, or a principle.
Trotz der Kritik beharrte der Politiker auf seinem Standpunkt.
Despite the criticism, the politician insisted on his position.
The meaning 'an einem Ort verweilen' (to remain in a place) is very rare today and is used almost only in literary or elevated texts. In everyday language, you almost exclusively encounter 'beharren auf' (to insist on).
Der Soldat beharrte auf seinem Wachtposten, bis die Ablösung kam.
The soldier remained at his guard post until the relief arrived.
to stay / remain
'bleiben bei' and 'beharren auf' can both express that someone does not change their opinion, decision, or demand. 'bleiben bei' is more neutral and often sounds calm: you simply stick with something. 'beharren auf' is stronger. It shows that someone is very persistent and does not want to give in. For normal decisions, 'bleiben bei' often fits well. If resistance or an argument is noticeable, 'beharren auf' is more precise.
Der Kunde beharrt auf einer schnellen Lösung.
The customer insists on a quick solution.
Sie bleibt bei ihrem Vorschlag, obwohl die anderen noch zweifeln.
She is sticking with her proposal, even though the others still have doubts.