Bash script regex on parameter

Question

I have a script like this:

#!/bin/bash                                                                                                                                                                                                                            
                                                                                                                                                                                                                                   
REGEX='(www\.)?\w*\.\w*'                                                                                                                                                                                                               
                                                                                                                                                                                                                                   
echo "$1" | grep -P -o $REGEX                                                                                                                                                                                                          
                                                                                                                                                                                                                                   
DOMAIN="$1" | grep -P -o $REGEX                                                                                                                                                                                                        

echo $DOMAIN    

What I want to achieve is to get the domain from a full URL.

If I give as parameter the: http://example.com/ then I need the example.com

The first echo works.

How could I pass that expression into a variable? I need to pass later the DOMAIN to a script.