Here is the outline of the code for objective function
objectiveFunction (Conductivity)
-- Use the above code you mentioned and get an estimate for U
-- compare that U with the actual U that you have (calculate the differences)
-- (possibly) reduce the difference into one number such as RMSE or MSE or whatever measure that you like
end of objectiveFunction
Now pass the objectiveFunction to your minimizing function let's say fminsearch (since you mentioned you want to use nelder-mead. That way it changes cond until it gets the best match for numerical solution and the actual solution.
Pretty much you need to run the above code many times. Make sure the cond is not hard coded in the solver part. You can make the code more flexible if you want like having variable domain size or solution etc. start with the simplest.
