Nikon did not include any information about lens hoods or filters anywhere in the documentation for your Nikon CoolPix L820. I don't see any reference to a filter thread either.
Many cameras in this category were regarded as an 'everything you need to take photos' item. The use of modern lens coatings were so improved by then that a lens hood was largely unnecessary.
There are several concerns involved in fitting a hood to this sort of lens - a hood that slips over the end of the lens as opposed to screw in will block the action of the zoom in full retraction and probably cause damage, so this approach is best avoided.
If there is an internal thread at the end of the lens you may be able to find something to fit, however the hood must be shallow enough to be useable at wide angle, which will mean that it will have limited effect at longer focal lengths.
Some hoods I have owned for other cameras are made of a rubber like material and can be pushed back for wa use and pulled out for tele use.
In a few cases where I have used this class of cameras the manufacturer has warned about attempting to fit filters hoods etc as the weight at full tele is magnified by the extended lens and can potentially cause damage or affect focussing performance. Nikon doesn't seem to have issued any such warning.
So thats the health warnings.
My Nikon B700 looks very like a slightly more modern version of your camera and has a clip in lens cap. I am aware that JJC makes an adaptor for my camera that allows it to take 62mm screw mount filters or lens caps.
My lens cap is an LC-CP29 - yours is an LC-CP28 I believe which implies it is a diifferent size so the adaptor that fits my camera wouldn't be any use to you and in my brief research I wasn't able to locate a similar adaptor for your camera.
So it is clearly not a straightforward thing you are asking for, but it probably is worth a bit of time checking.
There are also companies in the UK who manufacture rare adaptors and you will probably find the same thing in the USA.
There is always the depressing thought that after doing all this that it is possible that you may not see much difference - it can happen.
So there is a brief? summary of the info I have on your question.
I personally don't actually use a lens hood on my B700 but have been known to hold a piece of card in one hand to shade the lens, keeping it just outside of the image area.
Best of luck with your quest!