Tutorial Part C, 02-runge-kutta; error estimator

[moni]

Hey, 
I'm still working on my composition on time integration methods (in particular runge-kutta) also using Hermes2d. I'd like to compare numerically a few methods (Implicit_SDIRK_2_2, Implicit_Crank_Nicolson_2_2, Implicit_SDIRK_CASH_3_23, Implicit_SDIRK_CASH_5_24) using the tutorial part C-transient.
So far I tried to count the CPU-time with clock () and compared respectively the values. I also compare the graphics at specific timesteps (t=28800.00 s, t=57600.00 s, t=85500.00 s). But like "there's no proof with pictures" I'm looking for some error estimator. Is it possible to get an error estimator in this programme? I'm not sure if there's one for the first two methods above. But the embedded methods already have two approximations, haven't they? So can I use the two approx. maybe to make an aposteriori error estimation? How can I implement such one in the code?
Looking forward to your reply.
Regards,
Ramona

[Pavel Solin]

Hi Ramona,

On Mon, Oct 22, 2012 at 3:47 AM, moni <ramona...@gmx.de> wrote:

Hey, 
I'm still working on my composition on time integration methods (in particular runge-kutta) also using Hermes2d. I'd like to compare numerically a few methods (Implicit_SDIRK_2_2, Implicit_Crank_Nicolson_2_2, Implicit_SDIRK_CASH_3_23, Implicit_SDIRK_CASH_5_24) using the tutorial part C-transient.
So far I tried to count the CPU-time with clock () and compared respectively the values. I also compare the graphics at specific timesteps (t=28800.00 s, t=57600.00 s, t=85500.00 s). But like "there's no proof with pictures" I'm looking for some error estimator. Is it possible to get an error estimator in this programme?

All Benchmarks in the repository hermes-examples have an exact solution, convergence 

curves in both DOF and CPU time, etc. Can you please look there?

 

I'm not sure if there's one for the first two methods above. But the embedded methods already have two approximations, haven't they? So can I use the two approx. maybe to make an aposteriori error estimation? How can I implement such one in the code?
Looking forward to your reply.

Pavel

 

Regards,
Ramona

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Pavel Solin

Associate Professor

Applied and Computational Mathematics

University of Nevada, Reno

http://hpfem.org/~pavel