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Dienstagabend is a noun, but somehow used in an adverbial way here – why is it capitalized?
Is it the same like saying "Sie kommt nachher"? (Although no one would write "Sie kommt Nachher", from "das Nachher"...)
What's the name of this grammatical construct?
The adverbial version of Dienstagabend is dienstagabends. The former is a noun, the latter an adverb. The former should be capitalized, the second shouldn't. Nevertheless they differ in meaning:
Sie kommt Dienstagabend
means that she comes once, when? This (or specified by the context) Dienstagabend, which is not an adverb, but a time complement. On the other hand
Sie kommt dienstagabends
means, she usually comes on tuesday afternoons.
With nachher, it seems the inverse process: das Nachher is a nominalized adverb nachher.
Because "Dienstagabend" as a noun-noun compound is 100% a noun.
The sentence is lacking an "am" which is and can be also said as "an dem" ("on the") and then you could use the article rule that with most of the cases, a noun or a nominalized word will follow somewhere that you'll have to capitalize. The one main exception would be superlatives of adjectives ("am besten") ("at best") which can't be split up into "an dem" Besten ("at the best" in this case) and therefore stays with lowercases, since it's a trait on a question that could be asked with "wie" ("how") and not a matter that could be asked with "wer/wen/wem oder was"/"wessen" ("who/whom or what" /"whose").
You can also take a look at the official rules mentioned in the Duden, the German pendant to the Oxford Dictionary: http://www.duden.de/sprachwissen/rechtschreibregeln/Gro%C3%9F-%20und%20Kleinschreibung
