Troops: I have
reviewed and commented individually on your lab 12 reports. More than half
the class got things pretty correct, with a couple firmly documenting the
asymptotic convergence rate of near order 3 for the TWS solution at finer M
meshes for Pe = 1000. FYI, the
theory underlying the TWS algorithm predicts linear basis convergence rate is 4
on a sufficiently refined mesh good stuff!

In general, about half of the reports comparing the GWS and TWS solutions
plots for all M for Pe = 10 show no difference, which is correct with both being
non-monotone for M < 40^2. Note
further that for all M > 40^2, GWS and TWS solutions appear identical (some
reported no convergence good!) which means the algorithms produced an
interpolation of the exact solution!!
Hence the computed
convergence rate dropped to near zero precisely correct! On this point, always plot convergence
data on a semi-log plot NOT linear as almost everyone did
!

Continuing, some plots for solutions at Pe=1000 are also not monotone
which means you implemented the TWS algorithm incorrectly, most likely missing
the h^2 multiplier in the beta term.
Others apparently missed the square on this term, producing overly
diffused solutions for larger M.
Seems like you would have noticed these discrepancies in comparison to
plots in the Courseware! As the result, you missed the point about smooth
NOT necessarily being correct in GWS vs TWS comparisons at Pe=1000. The TWS solution (only) is engineering
accurate for any mesh M > 40^2

.

There are three key points with this computer lab exercise. The first remains, you get out what you
put in which means input coding errors are fatal. The second is that the TWS beta term for
small Pe does not influence the GWS solution at all, as the theory
predicts! The third is that use of
the solution adapted non-uniform meshing process with the TWS algorithm could
produce the precisely correct monotone solution at Pe = 1000 on an M = 20^2
mesh!

There are a few of you who failed to mount
this report, which earned you a 0/6 grade.
The archive is open. Recall we meet Thursday for class
wrap-up. AJB