Ground elder, also called bishop's weed and goutweed, is an extremely invasive perennial weed from Europe with a variegated ornamental form that is sold as a ground cover and should not be. The species spreads by brittle white rhizomes under and through everything in a bed, 12 to 18 inches high, in any soil and any light, and once it is in among the roots of shrubs and perennials it is close to impossible to get out.
The variegated cultivar 'Variegatum' is more restrained and attractive but still vigorous, and it reverts to the plain green form, which then runs. If you must have it, confine it to a container on paving or a bed walled by concrete, and never put the roots in the compost.
To remove it, the only reliable methods are patience and exclusion: dig out every piece of rhizome you can find (each fragment regrows), then cover the area with cardboard and a thick mulch, or black plastic, for a full growing season, and pull every shoot that finds light. Lifting the perennials in an infested bed, washing their roots bare and replanting elsewhere is sometimes the faster route. The flat white umbels in late spring look like elderflower and feed hoverflies, which is the kindest thing to be said for it.