The Battle Frontier is a recurring post-match area in many Pokémon games that offers players the ability to battle high-level Pokémon trainers. In the fourth generation of Pokémon, Diamond and Pearl didn't have a Battle Frontier, but Platinum did. Since Brilliant Diamond and Shining Pearl are remakes of Generation IV games, some in the community speculated before the remakes were released that Battle Frontier might be present in the remakes.
However, like many other Platinum-exclusive elements, such as the Looker character, Battle Frontier is missing from the remakes. Instead, you can visit the Battle Tower, which previously featured in the original versions of Diamond and Pearl, and was later transformed into a section of the Battle Frontier in Platinum. At the tower, you can face multiple trainers in a row as you earn battle points, which you can use to purchase various items in the battle tower shop.
The exclusion of Battle Frontier can probably be attributed to the area not present in the original versions of Diamond and Pearl. This omission might be a disappointment to some, but there are still a few things to do after the game, such as earning / completing the National Pokédex, catching Legendary Pokémon in Ramanas Park, and hanging up the game's Gym Leaders.