TY - THES A1 - Krebs, Andreas T1 - On solving nonlinear variational inequalities by p-version finiteelements N2 - This thesis introduces and analyzes a p-version FEM for variationalinequalities resulting from obstacle problems for some nonlinearelliptic partial differential operators. We approximate the solutionby controlling the obstacle condition in images of the Gauss-Lobattopoints. We show existence and uniqueness for thediscrete solution u_p from the p-version for the obstacle problem. Weprove the convergence of u_p towards the solution with respectto the energy norm, and assuming some additional regularity for thesolution we derive an a priori error estimate. In numericalexperiments the p-version turns out to be superior to the h-versionconcerning the convergence rate and the number of unknowns needed toachieve a certain exactness of the approximation. KW - Variationelle Ungleichungen KW - hp-Finite Elemente Methoden KW - a posteriori Fehlerschätzer KW - großskalierte Minimierung Y1 - 2004 UR - http://edok01.tib.uni-hannover.de/edoks/e01dh04/476288029.pdf 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 - TY - JOUR A1 - Krebs, Andreas A1 - Graeff, Christian A1 - Frieling, Isolde A1 - Kurz, Bodo A1 - Timm, Wolfram A1 - Engelke, Klaus A1 - Glüer, Claus-C. T1 - High resolution computed tomography of the vertebrae yields accurate information on trabecular distances if processed by 3d fuzzy segmentation approaches Y1 - 2008 ER - TY - GEN A1 - Bär, Werner A1 - Bäde-Schumann, Ulrike A1 - Krebs, Andreas A1 - Cromme, Ludwig T1 - Rapid method for detection of minimal bactericidal concentration of antibiotics Y1 - 2009 ER - TY - JOUR A1 - Krebs, Andreas A1 - Graeff, Christian A1 - Frieling, Isolde A1 - Glüer, Claus-C. T1 - In vivo Messung der Trabekelabstände von Wirbelkörpern mittels hochauflösender CT Y1 - 2008 ER - TY - GEN A1 - Pena, J. A. A1 - Graeff, Christian A1 - Krebs, Andreas A1 - Glüer, Claus-C. T1 - Cross-calibration of different reconstruction kernels for vertebral trabecular microstructure measures on a clinical CT under in-vivo like settings Y1 - 2009 ER - 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 - Schnell, R. A1 - Graeff, Christian A1 - Krebs, Andreas A1 - Glüer, Claus-C. T1 - Changes in crosssectional area of spinal canal and vertebral body under 2 years of teriparatide treatment: Results from the EUROFORS study Y1 - 2010 UR - http://www.springerlink.com/content/v81246127508l743/fulltext.pdf 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 - CHAP A1 - Futterer, Birgit A1 - Zaussinger, Florian A1 - Krebs, Andreas A1 - Egbers, Christoph T1 - Non-linear effects and associated instabilities in spherical Rayleigh-Benard experiments with variation of the viscosity contrast Y1 - 2011 ER -