Hello Hai,
what do you mean by weak and strong convergence rate?

A student of my checked the L2 error for refined grids and time steps
with the Richards equation and the FV method. We got the expected first
order convergence.
You can find the detail in his Bachelor's thesis, but it is German
"Baccour, M.H.: Verifikationsproblem mit bekannter Lösung für die
Zwei-Phasen-Darcy-Gleichung"

Additional there was a Master's thesis by Markus Wolff, it's written in
English and might help. I haven't checked myself, Bernd told me that:
"Wolff, M.: Comparison of mathematical and numerical models for twophase
flow in porous media."

Just out of curiosity: What's your affiliation?

Bye,
Christoph

-- 
GDB does hate your application, expresses its contempt through the
design of its command-line interface.   -- Tom Tromey, FOSDEM 2014

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