When you set up Ubuntu Server using the installer, Ubuntu sets the default root volume size to 100 GB. I realized this after I had already configured Ubuntu, so I needed to fix this mistake while the server was running.
First, you need to tell LVM to extend the volume to the maximum size available.
sudo lvextend -l +100%FREE /dev/ubuntu-vg/ubuntu-lv
Finally, you need to resize the root file system.
sudo resize2fs /dev/mapper/ubuntu--vg-ubuntu--lv
Your volume has now been resized to use the maximum available space.