Reference: https://www.w3.org/TR/NOTE-datetime

Uses joda-time (because yes, I still work in Java 1.6).  There is probably a simpler way.  But this works. This assumes all parts of the string are supplied.

public static Date convertUTCStringToLocalDateTime(String utcDate)
{
    DateTime utcDateTime = new DateTime(utcDate);
    Date localDateTime = utcDateTime.toDate();
    return localDateTime;
}