First of all, you dont need to put a tag name infront of the jQuery, unless you have other elements with exact same id on other elements, in other pages.
Next, your statement div_element.innerHTML = loading_anim;
is correct. So, the only explanation is that, there is no element with that ID, in the DOM.
Finally, since you are usign jQuery already, no need to mix up native JS and jQuery to create a dirty looking code.
function showLoading(id) {
div_element = $("#" + id);
console.log(div_element); //check the console to see if it return any element or not
div_element.html(loading_anim);
}