A Posteriori Error Estimator Competition for Conforming Obstacle Problems

Carsten Carstensen , Christian Merdon

MSC 2000

65N15 Error bounds

35J85 Unilateral problems and variational inequalities for elliptic PDE

Abstract
This paper on the a posteriori error analysis of the obstacle problem with affine obstacles and Courant finite elements compares five classes of error estimates for accurate guaranteed error control. In order to treat interesting computational benchmarks, the first part extends the Braess methodology from 2005 of the resulting a posteriori error control to mixed inhomogeneous boundary conditions. The resulting guaranteed global upper bound GUB involves some auxiliary partial differential equation and leads to four contributions with explicit constants. Their efficiency is examined affirmatively for five benchmark examples.