How do I make a registered domain name resolve to a local/private IP address

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http://unix.stackexchange.com – I have a Debian Linux server running on my local network. I also have port forwarding set up on my router so that computers outside my network can use my domain name and get to my website/FTP/SSH Server. That works perfectly. When I enter the domain name (or even the public ip address) on the local network however, it times out. To make it work I use the private IP address of the server when at home. This works ok, but it makes things a bit messy. If it's possible I'd like that domain name to resolve to the private address when on the local network. I've done a fair bit of Google searching (HowTos)