Steps 1+2 performed on host system in console window with root user:

1. Increase Disk Space of Virtual Drive (e.g. resize Virtual Drive vm1disk1.vdi to 120GIB):

   $ VBoxManage modifyhd vm1disk1.vdi --resize 122880

2. Increase RAM (e.g. resize Memory for VM vm1 to 8GIB):

   $ VBoxManage modifyvm vm1 --memory 8192

Steps 3-9 performed on guest system in console window with root user:

3. Resize partition for lvm (e.g. adjust partition /dev/sda2 to new size).

   Delete old partiton and create new, larger partition:

   $ fdisk /dev/sda
   Command (m for help): d
   Partition number (1-4): 2
   Command (m for help): n
   
   Command action
   e   extended
   p   primary partition (1-4)
   p
   Partition number (1-4): 2
   First sector (155-2097151, default 155): 
   Using default value 155
   Last sector, +sectors or +size{K,M,G} (155-37786, default 37786): 
   Using default value 37786
   
   Command (m for help): w

Reboot the system

4. Make enlarged partition available for LVM

   $ lvm
   lvm> pvdisplay
   --- Physical volume ---
   PV Name               /dev/sda2
   VG Name               vg_vm1
   PV Size               19,51 GiB / not usable 3,00 MiB
   ..
   lvm> pvresize /dev/sda2
   Physical volume "/dev/sda2" changed
   1 physical volume(s) resized / 0 physical volume(s) not resized
   lvm> pvdisplay
   --- Physical volume ---
   PV Name               /dev/sda2
   VG Name               vg_vm1
   PV Size               119,51 GiB / not usable 716,00 KiB
   ..
   lvm> vgdisplay
   --- Volume group ---
   VG Name               vg_vm1
   System ID             
   Format                lvm2
   .. 
   VG Size               119,51 GiB
   ..

5. Increasing logical volume for swap by 6GIB (from 2 to 8GIB):

   $ lvm
   lvm> lvdisplay
   ..
   --- Logical volume ---
   LV Path                /dev/vg_vm1/lv_swap
   LV Name                lv_swap
   VG Name                vg_vm1
   ..
   LV Size                2,00 GiB
   ..
   lvm> lvresize /dev/vg_vm1/lv_swap -L +6144M
   Size of logical volume vg_vm1/lv_swap changed from 2,00 GiB (512 extents) to 8,00 GiB (2048 extents).
   Logical volume lv_swap successfully resized

6. Increasing logical volume for root file system by adding the remaining space of partition:

   $ lvm
   lvm> lvdisplay
   --- Logical volume ---
   LV Path                /dev/vg_vm1/lv_root
   LV Name                lv_root
   VG Name                vg_vm1
   .. 
   LV Size                17,51 GiB
   ..
   lvm> lvresize /dev/vg_vm1/lv_root -l +100%FREE
   Size of logical volume vg_vm1/lv_root changed from 17,51 GiB (4482 extents) to 111,51 GiB (28546 extents).
   Logical volume lv_root successfully resized
   lvm> lvdisplay
   --- Logical volume ---
   LV Path                /dev/vg_vm1/lv_root
   LV Name                lv_root
   VG Name                vg_vm1
   .. 
   LV Size                111,51 GiB
   ..
   --- Logical volume ---
   LV Path                /dev/vg_vm1/lv_swap
   LV Name                lv_swap
   VG Name                vg_vm1
   ..
   LV Size                8,00 GiB
   ..

7. Analyze Swapping:

   $ swapon -s
   Filename	Type		Size	Used	Priority
   /dev/dm-1	partition	2097148	0		-1
   $ ls -l /dev/mapper
   total 0
   crw-rw----. 1 root root 10, 236  7. Apr 16:13 control
   lrwxrwxrwx. 1 root root       7  7. Apr 16:13 vg_vm1-lv_root -> ../dm-0
   lrwxrwxrwx. 1 root root       7  7. Apr 16:13 vg_vm1-lv_swap -> ../dm-1

8. End Swapping:

   $ swapoff -v /dev/vg_vm1/lv_swap
   swapoff für /dev/vg_vm1/lv_swap

9. Create and show new Swap space:

   $ mkswap -f /dev/vg_vm1/lv_swap
   Setting up swapspace version 1, size = 8388604 KiB
   no Label, UUID=..
   $ swapon -va
   swapon für /dev/mapper/vg_vm1-lv_swap
   swapon: /dev/mapper/vg_vm1-lv_swap: found swap signature: version 1, page-size 4, same byte order
   swapon: /dev/mapper/vg_vm1-lv_swap: pagesize=4096, swapsize=8589934592, devsize=8589934592
   $ swapon -s
   Filename				Type		Size	Used	Priority
   /dev/dm-1               partition	8388604	0	-1

Shutdown Guest system and boot with Linux live system (e.g. CentOS).

Steps 10-12 performed with Linux live system

10. Analyze file system structure:

    [centoslive@livedvd ~]$ su -
    [root@livedvd ~]# fdisk -l
    
    Disk /dev/sda: 128.8 GB, 128849018880 bytes
    ..
       Device Boot      Start         End      Blocks   Id  System
    /dev/sda1   *           1         155      512000   83  Linux 
    /dev/sda2             155       37786   125314356   83  Linux 
    ..
    Disk /dev/mapper/vg_vm1-lv_root: 119.7 GB, 119730601984 bytes
    ..
    Disk /dev/mapper/vg_vm1-lv_swap: 8589 MB, 8589934592 bytes
    ..

11. File system check of LVM file system

    [root@livedvd ~]# e2fsck -f /dev/mapper/vg_vm1-lv_root
    e2fsck 1.41.12 (17-May-2010)
    Pass 1: Checking inodes, blocks, and sizes
    Pass 2: Checking directory structure
    Pass 3: Checking directory connectivity
    Pass 4: Checking reference counts
    Pass 5: Checking group summary information
    /dev/mapper/vg_vm1-lv_root: 205089/1148304 files (0.1% non-contiguous), 2013043/4589568 blocks

12. Adjust root file system to size of logical volume

    [root@livedvd ~]# resize2fs /dev/mapper/vg_vm1-lv_root
    resize2fs 1.41.12 (17-May-2010)
    Resizing the filesystem on /dev/mapper/vg_vm1-lv_root to 29231104 (4k) blocks.
    The filesystem on /dev/mapper/vg_vm1-lv_root is now 29231104 blocks long.