Round-off errors relative to mesh size and polynomial order

mathematics
1

Hello everyone,
I am conducting a convergence study on the L2 norm of the error using the ‘errornorm’ function for polynomial orders 1, 2, 3 and 4. I am noticing that as soon as the L2 error for polynomials of order 4 is expected to drop below 10^-11 on a given grid, I start losing convergence. Did anyone observe a similar behavior? Is there some empirical relationship between round-off errors, mesh size and polynomial order? I am running a 2D Poisson problem and I start observing this phenomenon for structured triangular grids larger than 256x256 elements.

Thank you in advance.

2

You’ve hit machine precision.

3

Thank you Nate. Do you know though of any back of the envelop calculation to determine the smallest sized grid that I run a simulation on given a certain polynomial order and a starting residual?

Thanks again.