How to extend an ext3 partition over LVM inside a file (virtual machine)?

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http://unix.stackexchange.com – I need to extend the root partition of a virtual machine (VM) using LVM (Logical Volume Manager) . I can afford a few minutes of downtime so a VM shutdown/reboot is fine. The virtual hard disk is in qcow2 format but I can translate it to a raw format easily if it helps. Search engines (read: google) did not help that much because answers usually refer to using a LVM partition to host the virtual hard disk, here the LVM partition is inside the virtual hard disk which is a simple file... The virtual machine is running with linux-kvm and must stay bootable after the operation. Thanks for a (HowTos)