select2.val code example

Example 1: select2 dropdown with option to add new item

$('#select2')
    .select2()
    .on('select2:open', () => {
        $(".select2-results:not(:has(a))").append('<a href="#" style="padding: 6px;height: 20px;display: inline-table;">Create new item</a>');
})

Example 2: select 2 select a value

SELECT2 V4 :
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For select2 v4 you can append directly an option/s as follow:

<select id="myMultipleSelect2" multiple="" name="myMultipleSelect2[]">
    <option value="TheID" selected="selected">The text</option>                                                                   
</select>

Or with JQuery:
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var $newOption = $("<option selected='selected'></option>").val("TheID")
					.text("The text")
 
$("#myMultipleSelect2").append($newOption).trigger('change');

other example :
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$("#myMultipleSelect2").val(5).trigger('change');