to know perfectly well

• 明知山有虎，偏向虎山行

  insist on taking on a challenge, knowing perfectly well the dangers involved; go into the hills knowing perfectly well that there are tigers there(literal)

• 你们明知这样不对，为什么事先不告诉我们？

  Since you knew full well that this isn't right, why didn't you forewarn us?