A new subdomain-based error estimator for finite element approximations of elliptic problems.

In this talk we present a sub-domain residual error estimator for
finite element approximations of elliptic problems. It is obtained by
solving local problems on patches of elements in weighted spaces and
provides for an upper bound on the energy norm of the error when the
local problems are solved in sufficiently enriched discrete spaces. A
guaranteed lower bound on the error can also be derived by a simple
postprocess of the solutions to the local problems.
We will present several numerical tests and discuss the reliability and
performance of this estimator.
We will finally address the case of constrained elliptic problems, such
as the Stokes equations.