I'm wondering if FEniCS has a builtin function that can estimate the error between the solution it computes and the exact solution of a given PDE when the exact solution isn't known. Thanks.
Yes, look at the following demo:
http://fenicsproject.org/documentation/dolfin/1.5.0/python/demo/documented/auto-adaptive-poisson/python/documentation.html
Thanks for your quick response. I've looked at that demo and I see how it outputs a table that contains the error estimate at each iteration. Is there a way to output this number without using the auto adaptive solver?
Let me add that I would like to be able to save the estimated error to a file.
No you need to use the auto-adaptive solver (or implement your own error estimator).