Ex army wife here.
3 weeks isn't hugely long but if you're Not used to it I can see it can be tough.
Top tips:
Focus on the positives: watch what you want on tv, make your favourite dinners, no smelly socks/sports kit for a few weeks... whatever helps
Mark on a physical calendar when he'll be back and cross it off with the kids, each day marked off is a day closer to him coming home. Also mark the halfway point and remind yourself you're on the downhill part
Keep busy - see friends and family, talk to them on the phone if kids in bed and feeling lonely, even write some letters (older relatives love getting letters, you can get the kids to join in too)
Be prepared for his return - no I don't mean kill the fatted calf! But realise that even though you're missing him he'll quite likely annoy the hell out of you when he gets back! Because you'll likely have found your "groove" at that point and he'll disrupt that plus the kids may play up for a few days so go easy on both of you if it's "bumpy" when he first gets back.
Crying sometimes is ok but don't dwell on things.
Genuinely hope that's helpful to you, he'll soon be back 