Hello, I'd like to Clarify some stuff regarding Godot and GPU
A standard Application with OpenGL works this way -
Hardware Layer (GPU) -> OS -> Driver -> Application -> driver -> Device Pheripheral
A standard Hardware, in this case, is a GPU which is responsible for an API called OpenGL which is the name for the specification that describes the behavior of a rasterization-based rendering system.
Since this part works for Other people who use OpenGL, then this doesn't seem to have any Problem.
As we can see, you use Ubuntu 16 (Probably). Ubuntu has a wide range of supporting Devices/Output. It's an OS responsible for Software and Hardware Resources Management.
I've seen many people using Ubuntu and Godot Works fine for them, so, Ubuntu doesn't has any Problem either.
(Update Ubuntu Distribution to be sure that all of it's older Graphics Related Bugs have been fixed)
1. You've to check if settings/Software Settings don't Conflict.
2. Try Resetting your System
3. Uninstallation of Unused/Rarely Used Softwares
For other Queries related to it, I'd recommend -
Here is a tutorial on Updating Ubuntu - Ubuntu Tutorials to Upgrade Ubuntu to Higher Version
These are the root Cause of 99% all Application Problems, but Luckily Drivers can be updated in order to Fix the Problem.
For your problem, you can check if others are having the same problem or not. Plus, you can report Graphics Card Driver Makers to fix that problem. Check this forum - Toms's Hardware
If you see, each and every Part of the Application is working Correct and you still face the issue, then head to Github - Godot Engine Issues.
Since other users aren't facing this problem, you've to check if the OS/Drivers aren't a problem behind this? If you directly open an issue, then it's most likely to be closed because it'd be difficult the reproduce the Problem again on a Working System.
Ensure that Monitor/Other Computer Parts/Extensions are working Properly and working Okay.
Warning - In any Case/Problem, A backup is strongly recommended.