Well, it isn't ground-elder.
That's about the sum total of my useful input on I.D. though

If it were North American I'd almost wonder if it were a goldenrod but I don't think you folks have wild goldenrod and in any case it doesn't look quite right for it.
As far as solving the problem: my hope would be that this is not "so" bad an infestation and you can continue to live with it on the basis you've been for the past few years, i.e. it is a mexican standoff between your rate of weeding and the weed's rate of regrowth. If you can go in one or more times per season and really root out as much as possible, as deeply and thoroughly as possible (e.g. with a fishtail weeder or garden fork), that will help you keep the upper hand.
If that is not the case, if you are losing the battle despite your very best efforts, then truthfully you sort of have three options:
One, you can give up and learn to be a brilliant container gardener. (Seriously.)
Two, you can cover the entire area (and as much surrounding area as can be sacrificed, as well) with heavy heavy plastic and/or carpeting or pavers (with mulch on top if you wish) for at least 3-5 years, ideally also digging an 18" trench around the smothered area and burying steel or aluminum flashing as a root barrier. During those 3-5+ years, hone your container gardening skills. At the end of that period, remove the plastic or carpeting and hope the stuff is all gone and doesn't reinvade under the root barrier (at least not more than you can notice and pull).
Three, you can take a week off work and dig up the entire area very very carefully with a fork (not spade) and hand-sift the dirt, removing all traces of any roots of anything. Put 18" deep aluminum flashing all around the area when you're done, as a root barrier, and hope you got it all and it doesn't reinvade.
If options two or three fail, go back to option one.
Sorry to be grim, but these brittle-rooted rhizomatous things can be
that serious of a pest. If the area isn't too badly infested (and the SURROUNDING area isn't much infested either) then you CAN get them under control by the above means, I've done it. However in some cases there is just too much there, or too much in the surrounding area that recolonizes as fast as you can clear the garden. Honestly, you can grow quite a lot in containers
Good luck, "have fun"

,
Pat