The Bible frowns on divorce but does not forbid it.
Yes this is correct.
What it does forbid is divorcing and remarrying.....except in cases of fornication. (Read Matthew 19.) So the only way according to the Bible you can remarry is if she has cheated on you (and leaving isn't cheating), or when she passes away. According to the Bible fornication (sexual sin) and death are the only things that can end a marriage. Regardless of what man's laws say.
Well now, the topic gets interesting from here. What if a spouse does not know if the other spouse cheated, or thinks the spouse cheated without objective proof? Is that good enough? Also, be advised that Mt 19 doesn't "forbid" divorce but just says that those who divorce have committed adultery, e.g., a sin.
I've had a number of pastors tell me that my STBXW sinned in initiating the divorce, especially the walking out without notice part. One of the NT books (Titus I think) commands we Christians to work things out with each other, and if one can't communicate with the other, then use a trusted 3rd party. She did none of these!
Some of these same pastors say that re-marrying is not a sin, especially if you are the LBS (left behind spouse). Just don't lose your Christian principles during the divorce process, dating, and the wooing of your next spouse. I am not a Biblical scholar so I'm not the one to cite chapter and verse. But the general thrust of these pastors is that God did not intend us to be without intimate connection with others, so especially if you are not the one who walked out, you should have no compunction about meeting someone else and remarrying.
Of course, even if remarrying is a sin, then is it a sin forever? Is it an unforgiveable sin? Of course not! There is only one unpardonable sin. So of course the act of a second marriage is something that can be forgiven.
But such is about the end of my biblical scholarship.