Welcome to this website! The numerical methods are widely used in physics, chemistry, and engineering. Especially the Finite element method.

I am interested in a posteriori error estimation for the finite element method.

There are so many different types of a posteriori error estimation:
residual-based estimates
averaging-based (ZZ) estimates
equilibrated fluxes estimates
equilibrated residual estimates
hierarchical estimates
heuristic estimates
...

I first worked with the residual-based a posteriori error estimation for the potential formulations in electromagnetism for my PhD-thesis, using the industrial code Code_Carmel.

Then I work in Inria in a postdoc position under the direction of Martin Vohralík, with the a posteriori estimate based on the equilibrated flux recontruction, using the scientific software Freefem++ .
That is why I have this occasion to work with Frédéric Hecht and why Martin would like to create this website.

Here you can find some implementation work about the a posteriori error estimation based on the equilibrated flux reconstruction in collaboration with Frédéric Hecht, as well as Martin Čermák.

The details about the theoretical part of the implementations work can be found here for the general a posteriori error estimation for the Laplace problem and the Stokes problem.

For the adaptive stopping criterion part, which is MORE INTERESTING !!!!

YOU CAN find it here for the $p$-laplace problem and here for the Stokes problem using an Uzawa algorithm.

A posteriori estimator for the discretization error

A posteriori estimator distinguishing different error components and adaptive stopping criteria