Q:

how to include rel="author" in your own website?

As far as I know the rel attribute should only be used with a link, so my current approach
<h1><span rel="author">Peter M......</span>'s website</h1>

seems to be invalid (even though it's working with Google's rich snippet validator). So how would I use the rel="author" attribute when I don't want to link to any external websites like g+, twitter, ... (a link (on my website) pointing to my own website doesn't quite make sense to me)

A:

Another option is to validate authorship with an email address if you have one for the domain of your site.
You said you don't want to use external links, but something like 
<link href='https://plus.google.com/[your G+ id]' rel='author'/> 
has worked fine for me. 
Schema.org is apparently quite unpredictable. You should probably mark a person as an author, which means you might need a lot of markup.

