I had trouble connecting my sql server to (LocalDB)\v11.0 with my Windows account. I ended up having to delete it and recreate it.
Open a cmd prompt
c:\sqllocaldb delete "v11.0" LocalDB instance "v11.0" deleted. c:\sqllocaldb create "v11.0" LocalDB instance "v11.0" created with version 11.0
If the database is in use, stop MSSQL service and try again.