Email Address Validation In Two Input Boxes

I am trying to create a script for checking that checks that the email address entered into two input boxes is the same when a submit button is clicked, I have these two input boxes
<input type="text" name="user_email" id="user_email" />
<input type="text" name="user_email2" id="user_email2" />

This javascript code
<script type="text/javascript">
var email1 = document.getElementById(user_email);
var email2 = document.getElementById(user_email2);
function checkEmail(){
if (email1 != email2){
alert("The two email addresses are not the same");
}}
</script>

And this code for the button
<input type="submit" name="submit" id="submit" onSubmit="checkEmail" />
However this code is not working.