How can one use experimental measurements to improve the accuracy of numerical simulations?
One can you Recursive Bayesian Estimation to integrate the experimental measurements and numerical simulation. The following post outlines a simple example of Recursive Bayesian Estimation applied to population growth simulations.
http://dataminingtheworld.blogspot.com.au/2014/04/koalas-vs-possums-modelling-biological.html
You can look for test correlation and model updating methods, that respectively formalize the way of comparing experimental and simulation data and modify the model to improve correlation. These are very general techniques in FE analysis, when you have a model.
If you do not have a proper model, you can build a surrogate model using statistical approach.
Vassili, your question is very unclear, especially its second part. Therefore
"to improve the accuracy of numerical simulations" simply use double precision arithmetic. Of course, this advice is generally incorrect, but, additionally, completely unrelated to experimental measurements. Maybe you have "error propagation laws" in mind?
Some simulation data management (SDM) systems allow you to import experimental results in a similar way to simulation results. Then, you can generate in an automated way comparison reports not only between simulations, but also between several simulations and experimental results.
If you do not have access to such rather sophisticated SDM systems, of course you can generate such comparisons manually.
Whether or not you are able to integrate experimental and simulation results also depends on the fact whether you are able to adapt the simulation software - or at least to parametrize the models used, or not. If yes, you can use parametrized studies with respect to the experimental results in order to find "best" parameters for your simulation study - say, using good old least squares approaches -, and/or develop new models that describe the interesting experimental findings better.
The latter approach is hard to formalize, but I regard it as at least as important as the parametrization stuff.
One could probably also use artificial neural networks (ANN) that have been trained with experimental data and simulation data in order to find the simulations closest to the experiments. How to build useful ANN depends also on your ingenuity and is not trivial if you really want to adapt such ANN to your specific questions.
In all these comparisons, one should try to compare including error estimates both for experimental and simulation data.
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