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.