I shall provide you with an explanation of the usage of these idioms:
1) "meet someone": to come together (with), either by design or by accident; encounter someone. It can also mean "to be introduced to (a person)".
E.g.: "I met him unexpectedly".
E.g.: "We met at the station".
E.g.: "I have not yet met your cousin".
2) "meet up with (one)": to meet or encounter someone, especially in a casual capacity.
E.g.: "I'm meeting up with my friend tomorrow for lunch, so I won't be around in the afternoon."
E.g.: "She met up with her former lover".
E.g.: "I met up with him at the mall yesterday to help him shop for a suit".
* NOTICE: As opposed to the phrasal verb "meet up with", only "meet" can be used in the sense of "encounter/be introduced to someone for the first time". In that regard, you should know that the usage of "meet" is broader than that of "meet up with". So is its meaning!
Hope that helps!!! :)