Touch events that behave exactly like mouse events while mouse dragging or touch moving.

gistfile1.js

// vars to keep track of the "mouse" during touchmove
var  mouseX;
var  mouseY;

// create the custom events so you can dispatch them later
var touchover = new Event("touchover");
var touchout = new Event("touchout");
var touchup = new Event("touchup");

var element = document.getElementById("dropTargetDivName");

// attach standard mouse events which fire when you drag onto, out of or drop on an element
element.addEventListener('mouseover',dragOverHandler);
element.addEventListener('mouseout',dragOutHandler);
element.addEventListener('mouseup',dropHandler);
// attach custom touch events, dispatched below
element.addEventListener('touchover',dragOverHandler);
element.addEventListener('touchout',dragOutHandler);
element.addEventListener('touchup',dropHandler);

// initialize
initializeTouchEvents(element);

// functions called from both mouse and touch events
function dragOverHandler(e){
  // do whatever you want here
  this.style.border = "3px solid blue";
}
function dragOutHandler(e){
  // do whatever you want here
  this.style.border = "3px solid red";
}
function dropHandler(e){
  // do whatever you want here
  this.style.border = "3px solid green";
}

// THE PART YOU SHOULDN'T NEED TO TOUCH
function initializeTouchEvents(el){
  // during touchmove, check if you are dragging over or out of the element. Fire the event if you are.
  document.body.addEventListener('touchmove',function(e){
    var touch = e.touches[0];
    mouseX = touch.pageX;
    mouseY = touch.pageY;
    var rect = el.getBoundingClientRect();
    if(mouseX > rect.left && mouseX < rect.right && mouseY > rect.top && mouseY < rect.bottom){
      el.dispatchEvent(touchover);
    }else{
      el.dispatchEvent(touchout);
    }
  });
  
  // on touchend, check if you released on the element
  document.body.addEventListener('touchend',function(e){
    var rect = el.getBoundingClientRect();
    if(mouseX > rect.left && mouseX < rect.right && mouseY > rect.top && mouseY < rect.bottom){
      el.dispatchEvent(touchup);
      // hit the target
    }else{
      // missed the target
    }
  });
}