Let's say there is a numerical solution of the Laplace equation that was obtained using some complicated or unknown way, and we wish to estimate the error of this solution.
What would be a good way to do this?
I think we can start by plugging in the numerical solution into the Laplace equation, but then we obtain the error for the Laplacian of the function. We can then multiply it by the square of the area or volume of the function domain to estimate the error in the function itself.
Is that it, or is there a more standard or preferable method?