Numerical dispersion study via grid convergence and polynomial degree studies

I’d like to investigate numerical dispersion for a representative simple model (such as this one) and I am planning a grid convergence study. I would also like to investigate how the polynomial degree of the solver affects convergence and accuracy.

My current plan for how to measure accuracy is:

  • pick a point on the box mesh and generate its displacement time series
  • increase mesh resolution (2x, 4x, 8x, etc) to determine this point’s displacement time series at different resolutions

I would then repeat the grid convergence study from above with various polynomial degrees of the solver to see if that has an effect on convergence time/accuracy.

Is there a better/more useful measure of accuracy that I should use instead?

We prefer to check the convergence and error for a given resolution using the Method of Manufactured Solutions (MMS). We use these extensively for testing in the current main branch (will be PyLith v3.0.0); most of the current ones use a static problem but the test setup can handle time-dependent solutions. See Method of Manufactured Solutions — PyLith 3.0.0dev documentation for more information about the MMS tests.