The Chinese verbs 碰见 (pèngjiàn), 遇见 (yùjiàn) and 见面 (jiànmiàn) can be easy to get confused because of their similarity. Whilst all three words can mean "to meet", they're actually quite different in usage and grammar.
The first point to remember is that 碰见 and 遇见 are actually very similar to each other, whilst 见面 is very different.
碰见 and 遇见: unexpected encounters
碰见 and 遇见 are very similar in grammar and usage. Both of them mean "to meet", but in the sense of "to bump into" or "to meet unexpectedly". They're very similar in meaning, so don't worry too much about any differences between the two.
The other thing to remember about these two verbs is that they are transitive. You need to put an object after them.
jīntiān wǒ pèngjiànle yīgè lǎo péngyǒu.
Today I bumped into an old friend.
wǒ shàng gè xīngqí zài jùhuì shàng ǒurán yùjiànle tā.
I bumped into him at a party last week.
wǒ cónglái méi pèngjiànguò yīgè xiàng nǐ zhèyàng de nǚháir.
I've never met a girl like you before.
wǒ zuótiān zài chēzhàn yùjiànle yīgè shuàigē.
I met a handsome guy at the bus stop yesterday.
Hopefully you can get the sense that 碰见 and 遇见 are about bumping into people unexpectedly. You might already know the person or be meeting them for the first time, but the meeting was unplanned.
Also note how 碰见 and 遇见 always take an object.
见面: planned meetings
Unlike 碰见 and 遇见, 见面 is about meeting someone intentionally. This could be informally planning to see a friend or arranging to meet with your boss.
The other big difference between 见面 and 碰见 / 遇见 is that 见面 is intransitive. That is, it can't take any objects.
This means you have to use structures like this:
[subject] 跟 [noun] 见面
You can use other conjunctions instead of 跟, e.g. 和 (hé) or 与 (yǔ), but remember that you can't put any noun after 见面.
wǒ xīwàng wǒmen néng duō hé nǐ jiànmiàn.
I hope that we will see you more often.
wǒmen jiànmiàn shíjiān ānpái zài yī xīngqí hòu.
Let's arrange to meet in one week's time.
nǐmen jīngcháng jiànmiàn ma?
Do you often see each other?
wǒ xiǎng wǒmen yǐqián méi jiànguò miàn.
I don't think we've met before.
Translated from: chineseboost