The <base> element instructs the browser to append the URL in the href to all relative URLs on the page. So having:
<base href="http://www.example.com" />
Means that for :
<a href="#myid">here</a>.
The href is handled as :
http://www.example.com/#myid
Instead of
<current_page>/#myid
You almost certainly don't need that <base> element in the head section, especially based on your further point that using the full URL (which also has http://www.example.com in it) works, meaning your page is already at http://www.example.com and thus doesn't need to make it explicit with <base>.
Alternatively (and I don't actually recommend this, because your use of base seems incorrect), you could change the href of your link to be the current page plus the id hash, like:
<a href="mydocument.htm/#myid">here</a>.
As the browser will render the URL (when applying the base href) to :
http://www.example.com/mydocument.htm/#myid
and thus not try to leave the current page as it will treat it the same as if the base weren't set. (Note that this would only work when you have the base href set to the URL of the actual page's base, and as I mentioned earlier, that would make the base element unnecessary).
https://jsfiddle.net/ouLmvd3g/
If you are considering a javascript solution, since the <base> is apparently never necessary, I would recommend an event listener that removes the base element from the DOM rather than your suggested :
a fix using an event listener to remove the base URL for local links
A simple solution would be:
window.onload=function(){
var baseElement = document.getElementsByTagName("base")[0];
baseElement.parentNode.removeChild(baseElement);
}
https://jsfiddle.net/vLa0zgmc/
You could even add a bit of logic to check if the base element's href matches the current page's actual URL base, and only remove when it does. Something like:
var baseElements = document.getElementsByTagName("base");
if (baseElements.length > 0) {
var baseElement = baseElements[0];
var current_url = window.location.toString();
var base_url = baseElement.getAttribute("href");
// If the base url and current url overlap, remove base:
if (current_url.indexOf(base_url) === 0) {
baseElement.parentNode.removeChild(baseElement);
}
}
Example here : https://jsfiddle.net/gLeper25/2/