"closely adheres" is correct and usable in written English.
You can use it when referring to something that closely adheres to a certain standard or rule. For example, "The student closely adheres to the teacher's instructions."
I decided to begin at the beginning: the Magic Kingdom, which Disney opened in 1971, and which still closely adheres to Disney's families-first ethos.
Noh's best friend, the oafish Om, has a crush on an underclassman, the childlike Mick, who closely adheres to the uke stereotype.
The artist whose work most closely adheres to the theme is Joan Griswold, whose specialty is mundane subjects with prominent windows in them.
Another Combo THE Trump SoHo stands apart from the current crop of condo-hotels because it more closely adheres to the "condotel" model.
The film's depiction of Mr. Faraj being cornered by male operatives disguised in burqas, he said, closely adheres to his reporting.
It was observed that the composite coating displays a partial amorphous character and closely adheres to the WC matrix.
The titration algorithm was closely adhered to, as indicated by the close to 0 units mean and median differences between the titration algorithm dose and the prescribed dose (Supplementary Fig. 3).
The city closely adhered to that advice in restructuring its regulation.
(In his introductory comments Mr. Hamelin noted that the melody closely adhered to the German verse; a shame that printed texts were not provided).
Closely adhering to the San Andreas fault line, with the sky clearing and the top down, we corkscrewed our way toward the Golden Gate Bridge.
Andy Bull's enjoyable first work describes itself as a "nonfiction novel", which is an apt description for a book that, while closely adhering to historical fact, nevertheless allows itself plenty of authorial leeway in presenting those facts.
