Can you use JVM on web page

Me and my friend on college want to try and do a project where initially we make some web-page where two of us will have each separate account.

Then we would want to make feature where you can simultaneously edit code(Java), which you could compile and see output (as in for example NetBeans, Eclipse etc. and both of us could see it). It is designed to cooperate on some programming subjects.

My question is: Is it even possible? I figured you would need JVM to compile code. Can it be done and if yes what would be best practice?