I have the following partitions:
    root@test02 [~]# df -l
    Filesystem           1K-blocks    Used Available Use% Mounted on 
    /dev/mapper/vg_test02-lv_root
                         119277820 4947592 108274344   5% /
    tmpfs                   961132       0    961132   0% /dev/shm
    /dev/sda1               495844   54380    415864  12% /boot
    /dev/sdb1            103211296  714176  97254292   1% /tmp
    root@test02 [~]# fdisk -l
    Disk /dev/sdb: 107.4 GB, 107374182400 bytes
    255 heads, 63 sectors/track, 13054 cylinders
    Units = cylinders of 16065 * 512 = 8225280 bytes
    Sector size (logical/physical): 512 bytes / 512 bytes
    I/O size (minimum/optimal): 512 bytes / 512 bytes
    Disk identifier: 0x000448a6
       Device Boot      Start         End      Blocks   Id  System
    /dev/sdb1               1       13055   104856576   83  Linux
    Disk /dev/sda: 128.8 GB, 128849018880 bytes
    255 heads, 63 sectors/track, 15665 cylinders
    Units = cylinders of 16065 * 512 = 8225280 bytes
    Sector size (logical/physical): 512 bytes / 512 bytes
    I/O size (minimum/optimal): 512 bytes / 512 bytes
    Disk identifier: 0x0000c49e
       Device Boot      Start         End      Blocks   Id  System
    /dev/sda1   *           1          64      512000   83  Linux
    Partition 1 does not end on cylinder boundary.
    /dev/sda2              64       13055   104344576   8e  Linux LVM
    /dev/sda3           13055       15665    20971512+  8e  Linux LVM
    Disk /dev/mapper/vg_test02-lv_root: 124.1 GB, 124088483840 bytes
    255 heads, 63 sectors/track, 15086 cylinders
    Units = cylinders of 16065 * 512 = 8225280 bytes
    Sector size (logical/physical): 512 bytes / 512 bytes
    I/O size (minimum/optimal): 512 bytes / 512 bytes
    Disk identifier: 0x00000000
    Disk /dev/mapper/vg_test02-lv_swap: 4227 MB, 4227858432 bytes
    255 heads, 63 sectors/track, 514 cylinders
    Units = cylinders of 16065 * 512 = 8225280 bytes
    Sector size (logical/physical): 512 bytes / 512 bytes
    I/O size (minimum/optimal): 512 bytes / 512 bytes
    Disk identifier: 0x00000000
    root@test02 [~]# pvdisplay
  --- Physical volume ---
  PV Name               /dev/sda2
  VG Name               vg_test02
  PV Size               99.51 GiB / not usable 3.00 MiB
  Allocatable           yes (but full)
  PE Size               4.00 MiB
  Total PE              25474
  Free PE               0
  Allocated PE          25474
  PV UUID               GS07qb-CYuk-ywp9-A3C5-HoRt-HF9L-tlkJmc
  --- Physical volume ---
  PV Name               /dev/sda3
  VG Name               vg_test02
  PV Size               20.00 GiB / not usable 3.99 MiB
  Allocatable           yes (but full)
  PE Size               4.00 MiB
  Total PE              5119
  Free PE               0
  Allocated PE          5119
  PV UUID               dKk7VD-PZfO-9Zji-b8xq-WPP3-2tsG-sGJKFj
root@test02 [~]# vgdisplay
  --- Volume group ---
  VG Name               vg_test02
  System ID
  Format                lvm2
  Metadata Areas        2
  Metadata Sequence No  9
  VG Access             read/write
  VG Status             resizable
  MAX LV                0
  Cur LV                2
  Open LV               2
  Max PV                0
  Cur PV                2
  Act PV                2
  VG Size               119.50 GiB
  PE Size               4.00 MiB
  Total PE              30593
  Alloc PE / Size       30593 / 119.50 GiB
  Free  PE / Size       0 / 0
  VG UUID               kPHRMG-yF75-j7pW-H3fR-cIvb-eQXD-inhdvI
QUESTION: How can I extend my /dev/mapper/vg_test02-lv_root volume space using /dev/sdb1?
thank you very much
For extending the LVM disk, change your sdb type to Linux LVM by fdisk and then creates a physical volume of that disk: 
pvcreate /dev/sdb1
Then you have to extend the volume group which the logical disk is in and the check to extend correctly:
vgextend vg_group /dev/sdb1
vgdisplay
And for extending your logical disk:
lvextend /dev/vg_group/lv_disk /dev/sdb1
There is then one final step which is to resize the file system so that it can take advantage of this additional space, this is done using the resize2fs command.
resize2fs /dev/vg_group/lv_disk
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