I suspect this is a misuse from a non-native speaker.

Elapsed means to pass through or to go through. A good translation of this could be "...this article will give an insight going through different topics." But I have never used "elapsed" that way in conversation, and I think it would sound odd if used that way in conversation. ( I am from the US a native english speaker.)

Could I use work through instead of elapse through?

That use of "elapse" is wrong. "Elapse" is used to describe the passage of time. Example: Much time has elapsed since the Treaty of Rome was signed. The sentence is badly written anyway. "Aforementioned topic" combined with "different topics" is awkward. It would be better to say "discusses" or "reviews" rather than "will give an insight". In terms of the usage of "insight", "an insight into the [noun]" is the normal construction. When writing an abstract describing an article, we would normally just say, "This article reviews/discusses/examines [state specific subject(s)]."