If you have a variable containing a DOM element, and want to select elements related to that DOM element, simply wrap it in a jQuery object.
var myDomElement = document.getElementById( "foo" ); // A plain DOM element.
$( myDomElement ).find( "a" ); // Finds all anchors inside the DOM element.
Many people try to concatenate a DOM element or jQuery object with a CSS selector, like so:
$( myDomElement + ".bar" ); // This is equivalent to $( "[object HTMLElement].bar" );
Unfortunately, you cannot concatenate strings to objects.