On equilibrated residual error estimates

J. Schöberl, RWTH Aachen, Germany

Wednesday, November 12
at 16.15, HG E 1.1

A posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for a dual problem. A cheap computation of such functions via equilibration is well-known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to Maxwell's equations and edge elements. The two key ingredients are exact sequences for distributional finite elements, and a divergence free local decomposition of the residual.

For the scalar equation, we could recently prove that the efficiency of the proposed error estimate is uniform in the polynomial order. We give an outline of the proof, and present numerical results.

D. Braess and J. Schöberl: Equilibrated Residual Error Estimator for Maxwell's Equations. Math. Comp., 77(262), 651-672, 2008

D. Braess, J. Schöberl, V. Pillwein: Equilibrated Residual Error Estimates are p-Robust (submitted).