@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{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} } @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} }