Hello Hai,
as far as I know you usually look at strong convergence rates (every
strongly convergent sequence is also weakly convergent). That means
|u-u_h| -> 0 (in the corresponding Hilbert norm) implies strong
convergence. As Christoph already mentioned, for the box method you get
in general first order accuracy: second order for pressure which implies
first order for velocity and first order in time because of backward or
forward Euler method.
For the cell centered Finite Volume Scheme with Two-Point Flux
Approximation you only achieve this rates for isotropic permeability
tensors. If you want to achieve first order for general grids and
permeability tensors you can use Multi-Point-Flux approximations.
Regards,
Martin
On 11/24/2014 05:42 PM, Christoph Grüninger wrote:
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
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