I think you want to do this with silent finger changes, which is where you keep the key depressed, and without lifting the finger pushing the key down, switch the finger on that key, without striking it again. Silent changes are often given with the fingering in parenthesis.
So, the first bar is finger in L.H. 5 2 1
then the silent change on D3
from 1
to (5)
, which then gives you the reach of 5
to 1
for the octave leap, which should be a familiar leap, an octave played 5 1
.
The second bar also can a silent change, but without striking the key for the switch at all. D4
is played with L.H. 1
, reach down the octave to D3
and touch the key with (5)
, but don't actual press it down, only touch it silently, then again silently change (5)
to (1)
, then reach down yet another octave to D2
, and strike it to play aloud with 5
.
The strategy is to have the size of an octave well trained in your hands between fingers 5
and 1
. You want to be able to hit the octave interval automatically. Within the octave the other fingers should then be trainer for various positions and interval distances based on triads in root position, first inversion, and second inversion, or five finger positions of scale portions either ascending from the lower pitch or descending from the higher pitch. If you can "find" any of those chord/scale intervals within an octave reach, then you can use silent finger changes on the piano keys involved and get your hand moved into various new positions.
Depending on the tempo of the music you may not have time to do a proper silent finger change, but you can still use the basic concept. If you need to move quickly up to the D4
, you release 1
on D3
, hold the octave reach in the L.H. then sort of "remember" spatially where 1
was, and put 5
in the same place without loosing the octave stretch of your hand. If you keep the octave reach, you should be able to just put 1
down, and have it land on D4
.