TY - GEN A1 - Maischak, Matthias A1 - Krebs, Andreas A1 - Stephan, Ernst P. T1 - A quadratic programming problem arising from the p-version for obstacle problems T2 - Electronic Notes in Discrete Mathematics Y1 - 2010 SN - 1571-0653 VL - 36 SP - 923 EP - 930 ER - TY - GEN A1 - Krebs, Andreas A1 - Maischak, Matthias A1 - Stephan, Ernst P. T1 - Adaptive FEM-BEM coupling with a Schur complement error indicator T2 - Applied Numerical Mathematics KW - Adaptive finite element methods KW - adaptive boundary element methods Y1 - 2010 SN - 0168-9274 VL - 60 IS - 8 SP - 798 EP - 808 ER - TY - JOUR A1 - Krebs, Andreas A1 - Stephan, Ernst P. T1 - A p-version finite element method for nonlinear elliptic variational inequalities in 2D N2 - This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential operators. We approximate the solution by controlling the obstacle condition in images of the Gauss-Lobatto points. We show existence and uniqueness for the discrete solution u p from the p-version for the obstacle problem. We prove the convergence of u p towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation. KW - FEM Y1 - 2007 UR - http://www.springerlink.com/content/p1126727200545k8/fulltext.pdf U6 - https://doi.org/10.1007/s00211-006-0035-0 ER -