Add a new partition into LVM

sudo fdisk /dev/sda

# Create a new partition /dev/sda3

sudo pvcreate /dev/sda3

sudo pvdisplay

sudo vgdisplay

# ubuntu16044-vg is an existed volume group

sudo vgextend ubuntu16044-vg /dev/sda3

sudo vgdisplay

sudo lvdisplay

# /dev/ubuntu16044-vg/root is an existed logical volume

sudo lvextend -l 100%VG /dev/ubuntu16044-vg/root

sudo lvdisplay

sudo resize2fs /dev/ubuntu16044-vg/root [new_size]