Is marriage to a girl with whom one has had a relationship and who subsequently became pregnant valid according to Islamic law, and how can one repent and purify oneself from this act?

Some scholars stipulate for the validity of the marriage between an adulterer and the woman with whom he committed adultery, that both of them must have repented, and that she must not be pregnant. It is advisable to renew the marriage contract after repentance and after delivery to avoid scholarly اختلاف (disagreement). As for the child born of adultery, the majority of scholars state that he is not attributed to his biological father, the adulterer, but rather to his mother, and he is like a stepchild. However, some scholars hold the view that he is attributed to his biological father, the adulterer, if he marries his mother.