NonDocumentTypeChildNode.nextElementSibling

<div id="div-01">Это div-01</div>
<div id="div-02">Это div-02</div>

<script type="text/javascript">
  var el = document.getElementById('div-01').nextElementSibling;
  console.log('Сосед div-01:');
  while (el) {
    console.log(el.nodeName);
    el = el.nextElementSibling;
  }
</script>

// Источник: https://github.com/Alhadis/Snippets/blob/master/js/polyfills/IE8-child-elements.js
if (!('nextElementSibling' in document.documentElement)) {
    Object.defineProperty(Element.prototype, 'nextElementSibling', {
        get: function() {
            var e = this.nextSibling;
            while (e && 1 !== e.nodeType) {
                e = e.nextSibling;
            }
            return e;
        }
    });
}

// Источник: https://github.com/jserz/js_piece/blob/master/DOM/NonDocumentTypeChildNode/nextElementSibling/nextElementSibling.md
(function(arr) {
    arr.forEach(function(item) {
        if (item.hasOwnProperty('nextElementSibling')) {
            return;
        }
        Object.defineProperty(item, 'nextElementSibling', {
            configurable: true,
            enumerable: true,
            get: function() {
                var el = this;
                while (el = el.nextSibling) {
                    if (el.nodeType === 1) {
                        return el;
                    }
                }
                return null;
            },
            set: undefined
        });
    });
})([Element.prototype, CharacterData.prototype]);