@misc{PruefertTroeltzschWeiser, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8223}, number = {04-47}, abstract = {The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.}, language = {en} } @misc{Bornemann, author = {Bornemann, Folkmar A.}, title = {Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-880}, number = {SC-92-18}, abstract = {A new adaptive approach for one-dimensional scalar conservation laws with convex flux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to LAX. For arbitrary times, the solutions is represented by an adaptive monotone spline interpolation. The spatial approximation is controlled by local \$L^1\$-error estimated. As a distinctive feature of the approach, there is no discretization in time. The method is monotone on fixed grids. Numerical examples are included, to demonstrate the predicted behavior. {\bf Key words.} method of characteristics, adaptive grids, monotone interpolation, \$L^1\$-error estimates {\bf AMS(MOS) subject classification.} 65M15, 65M25, 65M50.}, language = {en} } @misc{LangWalter, author = {Lang, Jens and Walter, Artur}, title = {An Adaptive Discontinuous Finite Element Method for the Transport Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-579}, number = {SC-91-07}, abstract = {In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.}, language = {en} } @misc{Klapproth, author = {Klapproth, Corinna}, title = {The Contact-Stabilized Newmark Method - Consistency Error of a Spatiotemporal Discretization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15198}, abstract = {The paper considers an improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatiotemporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up no now, the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the assumption of bounded total variation of the solution. Here, interest focusses on the consistency error of the Newmark scheme in physical energy norm after discretization both in time and in space. The resulting estimate for the local discretization error allows to prove global convergence of the Newmark scheme under an additional assumption on the active contact boundaries.}, language = {en} }