i bet i get a lot of grief or get put on ignore for this, but here goes:
fast and pray. fast beyond sacrifice, here. pray for reconciliation, heart changes in both of you, humility, strength, & courage. if there was adultery, even, i would be loath to advise you to let him divorce you easily.. and you both especially have to fight for it, because you have the 4 children to consider...
it's not the fact that you are "staying married just for the kids" that is the big deal. the fact is that because you 2 have 4 children together, you two will never be out of each other's lives. your divorce is not just affecting you two--which by the way, i will tell you what i and most other people who divorce felt--but the children. and they cannot help but subconsciously take some blame for your divorce. for whatever reason, they will think that this is their fault, and they will understand that dad is abandoning them. there is nothing you can say or do, or the dad can say or do, to not make them feel like this. they will see their daddy as quitting. and you as quitting. and it affects them horribly.
and you?? you & he think it will be easier because you are not living together. and it won't. it will be more and more difficult. because you two don't have to compromise anymore. you don't have to get along. you don't have to stick it out, per se. and your children will be affected hugely by the lack of united fronts. then you two will have that option to turn around and meet and date other people. and this will cause even more turmoil for everyone involved, and worse yet, the sins you couldn't conquer in your first marriage, you will bring to your 2nd marriage, because they weren't dealt with.. they were just given up on.
if he has left, and he has no intentions of reconciliation, whether you do or not, then i say pray and fast for his heart. i say grieve and beg God for another chance. even if this were a "justifiable" divorce, after that original euphoria of relief, and this is done, and over, and amen, stage, then comes the grief, the hurt, the anger, the feeling of failure and worthlessness, and "i can't do anything right.. i failed at my marriage, i fail at being a good and right parent, i fail at being a godly woman, i fail at being righteous" etc etc etc. and you will think that stuff for at least 2 years, average.
and you will never get over the pain of the divorce. those 4 children will be your reminder for the rest of your life.
now, again, if we are talking about adultery here, then yes, this is a different story, to many extents.. and physical abuse cases, are individual--i know i will get grief for that... real grief...sorry, my opinion.... in cases of adultery and abuse, i still say pray and fast fast fast.. beg God for another chance. beg God for wisdom and knowledge humility and true love for your husband, and beg God for all of these things to be in your husband's heart, so you can restore this marriage...
and 
