Stabilization techniques and a posteriori error estimates for the obstacle problem

Biermann, D.1, a; Iovkov, I.1, b; Blum, H.2, c; Rademacher, A.2, d; Klein, N.2; Suttmeier, F.-T.2, e

1)
Institut für Spanende Fertigung, Technische Universität Dortmund, Baroper Str. 303, 44227 Dortmund
2)
Lehrstuhl für Mathematik X, Wissenschaftliches Rechnen, TU Dortmund, 44221 Dortmund

a) biermann@isf.de; b) iovkov@isf.de; c) heribert.blum@mathematik.tu-dortmund.de; d) andreas.rademacher@tu-dortmund.de; e) suttmeier@mathematik.uni-siegen.de

Kurzfassung

This work deals with a posteriori error estimates for the obstacle problem. Deriving an estimator on the basis of the variational inequality with respect to the primal variable, an inconsistent one is obtained. To achieve consistency, this problem is treated by a Lagrange formalism, which transfers the variational inequality into a saddle point problem. Different techniques to ensure the stability of the discretization and to solve the discrete problems by iterative solvers are studied and compared. Numerical tests confirm our results of consistent a posteriori error estimation

Schlüsselwörter

obstacle problem, finite element method, stabilization, a posteriori error estimate, variational inequality

Veröffentlichung

Applied Mathematical Sciences, 7 (2013) 127, S. 6329-6346, doi: 10.12988/ams.2013.39504