Advection-diffusion convergence issue

[bknight1]

With increasing resolution the error is not showing a convergence order:

The errors are concentrated at the diffusive boundary:
unknown (T) degree comparison:

diffusivity (D) value comparison:

To test any updates, the script to check convergence is found here

[lmoresi]

I had a look at this. I think it is unrealistic to start with a case which has an infinite gradient. I have an example notebook that looks at advection starting from a finite time and looking at the change over time and with advection. I'll upload and you can review.

[bknight1]

Keen to have a look!

[lmoresi]

@bknight1 Take a look at Jupyterbook/Notebooks/Examples-Convection/Ex_AdvectionDiffusion_1dBlock.py.

I'm careful to start from a finite time after the step-function initial condition is applied so that it can be represented reasonably well by the mesh (maybe less so for the simplex example shown). Move it / diffuse it and compare before the analytic solution becomes invalid.

[bknight1]

Makes sense! I'll update the script and see how it performs