The 1921 census can be found on Find My Past. Carl can be found on that census.
It looks very much as Arthur K has said that he married for a second time in 1920 - in Halstead, Essex to Lavinia Gardner.
The only possible death I can see for Louisa between 1911 and 1920 is showing on the Groindex as Louisa Petersen ( death age 65) Jul - Sep 1917 in Reigate, Surrey. It might be worth obtaining a digital image of this death to see if it is the correct one. ( I note that the surname for this death has been transcribed as Peterson on FindMyPast.).
William
Thank you so much for your help William, I will definitely be checking out the 1921 census on Find My Past.