"Meet" and "meet up" can be used interchangeably, but "meet up" is informal.
Likewise, "meet with" and "meet up with" can be used interchangeably. "With" acts as a preposition so it needs an object.
Although "up" and "with" are both prepositions, "up" tends to cling to "meet" and cease to act as a preposition, as if "meet up" were just one word, a verb.
But not always!
When you use "up" as a preposition, the meaning changes:
"Santa Claus is the name of the gentleman I met up north."