why is the ending of this demonstrative adj in -e not -er?

Question

Kommt, wir setzen uns auf diese Bank.

where die Bank, die Bänke is a bench in the park.

Shouldn't it be: auf dieser Bank ? Isn't it a strong adj. ending as to this Wikibook article?

Answer 1

In German, we have the two verbs sitzen and setzen that both translate to the English to sit. Sitzen is used when you are already sitting at the location, which is why it demands the dative case:

Wo sitzt ihr? – Wir sitzen auf dieser Bank.
_{(Where do you sit? – We are sitting on this bench.)}

Setzen, in contrast, is used to express that you are going to sit down, that is, you fulfill a movement towards the place. Therefore, setzen demands the accusative case:

Wohin setzt ihr euch? – Wir setzen uns auf diese Bank.
_{Where do you sit (down)? – We are sitting (down) on(to) this bench.}

Notice that dies is not an adjective but a demonstrative pronoun, which is why the rules of strong/weak/mixed adjective declension do not apply here.