@phdthesis{Krebs, author = {Krebs, Andreas}, title = {On solving nonlinear variational inequalities by p-version finiteelements}, abstract = {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.}, language = {de} } @article{KrebsStephan, author = {Krebs, Andreas and Stephan, Ernst P.}, title = {A p-version finite element method for nonlinear elliptic variational inequalities in 2D}, doi = {10.1007/s00211-006-0035-0}, abstract = {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.}, language = {en} } @article{KrebsGraeffFrielingetal., author = {Krebs, Andreas and Graeff, Christian and Frieling, Isolde and Kurz, Bodo and Timm, Wolfram and Engelke, Klaus and Gl{\"u}er, Claus-C.}, title = {High resolution computed tomography of the vertebrae yields accurate information on trabecular distances if processed by 3d fuzzy segmentation approaches}, language = {en} } @misc{BaerBaedeSchumannKrebsetal., author = {B{\"a}r, Werner and B{\"a}de-Schumann, Ulrike and Krebs, Andreas and Cromme, Ludwig}, title = {Rapid method for detection of minimal bactericidal concentration of antibiotics}, language = {en} } @article{KrebsGraeffFrielingetal., author = {Krebs, Andreas and Graeff, Christian and Frieling, Isolde and Gl{\"u}er, Claus-C.}, title = {In vivo Messung der Trabekelabst{\"a}nde von Wirbelk{\"o}rpern mittels hochaufl{\"o}sender CT}, language = {de} } @misc{PenaGraeffKrebsetal., author = {Pena, J. A. and Graeff, Christian and Krebs, Andreas and Gl{\"u}er, Claus-C.}, title = {Cross-calibration of different reconstruction kernels for vertebral trabecular microstructure measures on a clinical CT under in-vivo like settings}, language = {en} } @misc{MaischakKrebsStephan, author = {Maischak, Matthias and Krebs, Andreas and Stephan, Ernst P.}, title = {A quadratic programming problem arising from the p-version for obstacle problems}, series = {Electronic Notes in Discrete Mathematics}, volume = {36}, journal = {Electronic Notes in Discrete Mathematics}, issn = {1571-0653}, pages = {923 -- 930}, language = {en} } @misc{SchnellGraeffKrebsetal., author = {Schnell, R. and Graeff, Christian and Krebs, Andreas and Gl{\"u}er, Claus-C.}, title = {Changes in crosssectional area of spinal canal and vertebral body under 2 years of teriparatide treatment: Results from the EUROFORS study}, language = {en} } @misc{KrebsMaischakStephan, author = {Krebs, Andreas and Maischak, Matthias and Stephan, Ernst P.}, title = {Adaptive FEM-BEM coupling with a Schur complement error indicator}, series = {Applied Numerical Mathematics}, volume = {60}, journal = {Applied Numerical Mathematics}, number = {8}, issn = {0168-9274}, pages = {798 -- 808}, language = {en} } @inproceedings{FuttererZaussingerKrebsetal., author = {Futterer, Birgit and Zaussinger, Florian and Krebs, Andreas and Egbers, Christoph}, title = {Non-linear effects and associated instabilities in spherical Rayleigh-Benard experiments with variation of the viscosity contrast}, language = {en} }