Yes, this is ground elder or goutweed.  It is a groundcover that typically escapes and becomes a problem.  
Goutweed is a perennial plant in the Apiaceae (Carrot) family. This plant can form large colonies from underground rhizomes. Leaves are alternate, compound, with toothed-margined leaflets. Some plants may contain white-edged leaflets, but others will be green in color. It is usually the variegated form that is cultivated as an ornamental. Flowering structures of goutweed consist of fairly large, compound umbels with white petals.

Control of goutweed can be very difficult and will depend on its location. Digging up the root system and chopping the stems are certainly options for control, but regrowth should be expected. If herbicides are an option, repeated applications of glyphosate (Roundup, others) should be effective over time. It is important to use an herbicide that can kill the underground root system. There are also several “brush killers” on the market, such as Brush-B-Gon, that should provide control. The “brush killers” may not be ideal in flowerbeds. Multiple applications of these herbicides will be required. Remember, always read and follow labeled directions.

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