You’re close, but you don’t need the add_rewrite_rule
call.
add_action('init', 'wpse82004_init');
function wpse82004_init()
{
global $wp_rewrite;
$wp_rewrite->author_base="u";
$wp_rewrite->author_structure="https://wordpress.stackexchange.com/" . $wp_rewrite->author_base . '/%author%';
}
After that’s in place, just re-save permalinks.
Here’s a plugin to put an option on your permalinks page to do this.