You can use $.each() to loop through the array and append the variable to the ul
:
$(document).ready(function() {
var testArr = ["element 1","element 2","element 3","element 4"];
var listItem ="";
$.each(testArr, function(i, val) {
listItem += "<li>" + val + "</li>";
});
$('#myUL').html(listItem);
});