Elaborate as a a verb always means to build on something or add further detail. So you can always say "elaborate on something." If a person says to you: "would you care to elaborate?" What they mean is "would you care to elaborate on what you just said?" It means "go into more detail." In your example sentence they are talking about taking basic map problems and elaborating on them to talk about map problems with mobiles. It's a lot of words that hide the fact that they are actually saying "elaborate advanced stuff from simple stuff." The words to notice here are "elaborate" and "from." Its not elaborate by itself, but "elaborate from." It's correct English, but it's not very readable. The safest thing would be to always use "elaborate on" if you can.

‘Elaborate’ as a verb is most often intransitive. It is a common word meaning ‘talk more about’. Can you elaborate? (Can you explain in more detail?) He elaborated on the country’s vaccination strategy. (He talked about it some more.) ‘To elaborate something’ as a transitive verb is very rare. ‘We hired him to elaborate a strategy to enhance cyber security.’ (More common would be ‘work on’ or ‘develop’. ) It also has a biological meaning.

Can you elaborate?

Both are correct. Slightly different meanings... You can use 'elaborate' in the sense of creating, building, developing - e.g. a plan/ project. You can also use "elaborate on"to mean: building on an existing structure, idea, plan; to add to it - to give more dimensions/ layers/ complexity...