[Closed] website link checker tool?

My google fu is weak today.

I'm trying to check a website for dead links. Current method seems to be: open page, look for links, check they work, go to next page on list.

Seems to me there must be a way to automate this. I have a list of the individual pages in the overall site, but would really like to find something that will work through the whole site (domain?) and report errors so I can get them fixed.

I can't for a moment believe I'm the first to have this problem, is there a name for the thing that does this? Can you recommend a good (free) one? Am I thinking about it wrong?