Dear Fenics community,
I’m studying a 2D convection-diffusion problem with the finite element method. I noticed an unexpected trend in the RMSE when varying the grid size (see figure):
System Parameters:
- Domain: 10m × 10m
- Contaminant source: 2m × 2m (center)
- Time step: dt = 0.001s
- Total simulation time: 1s
- Grid size (dx): varies from 0.01 to 2.0m
Observation:
the RMSE first increases with dx up to about 0.2m, then unexpectedly decreases for larger dx values.
Has anyone encountered similar behavior or could explain this phenomenon? Is this related to the relationship between spatial discretization and round errors?
Thank you for your suggestions!