Speaker
Dietrich Braess
Description
Elliptic partial differential equations are often formulated as a variational problem, more precisely as a minimum problem for a suitable energy. A discretization by conforming finite elements provides an upper bound of the energy. Similarly the discretization of the dual variational problem yields a lower bound. The difference of the two energies provides an a posteriori error bound without generic constants with respect to the energy norm. We show that a useful approximate solution of the dual problem is obtained by a cheap postprocessing of the finite element solution of the primal problem. The procedure is easily understood for the Poisson equation. It is only slightly more involved for other differential equations.
