Lube, Gert

[["dc.bibliographiccitation.firstpage","211"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Computational and Applied Mathematics"],["dc.bibliographiccitation.lastpage","236"],["dc.bibliographiccitation.volume","132"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Mueller, L."],["dc.contributor.author","Otto, F. C."],["dc.date.accessioned","2018-11-07T08:52:31Z"],["dc.date.available","2018-11-07T08:52:31Z"],["dc.date.issued","2001"],["dc.description.abstract","A nonoverlapping domain decomposition algorithm of Robin-Robin type is applied to the discretized Oseen equations using stabilized finite element approximations of velocity and pressure thus allowing in particular equal-order interpolation. As a crucial result we have to inspect the proof of a modified inf-sup condition, in particular, the dependence of the stability constant with respect to the Reynolds number (cf. appendix). After proving coercivity and strong convergence of the method, we derive an a posteriori estimate which controls convergence of the discrete subdomain solutions to the global discrete solution provided that jumps of the discrete solution converge at the interface. Furthermore, we obtain information on the design of some free parameters within the Robin-type interface condition which essentially influence the convergence speed. Some numerical results confirm the theoretical ones. (C) 2001 Elsevier Science B.V. All rights reserved."],["dc.identifier.doi","10.1016/S0377-0427(00)00321-6"],["dc.identifier.isi","000169651500001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/22185"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.relation.issn","0377-0427"],["dc.title","A nonoverlapping domain decomposition method for stabilized finite element approximations of the Oseen equations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","S725"],["dc.bibliographiccitation.journal","ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK"],["dc.bibliographiccitation.lastpage","S726"],["dc.bibliographiccitation.volume","81"],["dc.contributor.author","Mueller, L."],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2018-11-07T09:40:49Z"],["dc.date.available","2018-11-07T09:40:49Z"],["dc.date.issued","2001"],["dc.description.abstract","We consider the nonstationary incompressible Navier-Stokes problem in a bounded domain. A semidiscretization in time followed by a linearization procedure lead to Oseen type problems. For an efficient solution we take advantage of a nonoverlapping domain decomposition method (DDM) with interface conditions of Robin type. Strong convergence of the DDM-iterations to the Oseen solution can be proven. Furthermore we apply an a-posteriori estimate which controls the error on the subdomains in terms of the jumps of the velocity across the interface. This may serve as a stopping criterion and gives some information how to choose a free parameter appearing in the interface condition. A stabilized FEM is used to derive a discrete version of the DDM and requires a modification of the method."],["dc.identifier.isi","000169246000137"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33583"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Wiley-v C H Verlag Gmbh"],["dc.publisher.place","Berlin"],["dc.relation.eventlocation","UNIV GOTTINGEN, GOTTINGEN, GERMANY"],["dc.relation.issn","0044-2267"],["dc.title","A nonoverlapping DDM for the nonstationary Navier-Stokes problem"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","91"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Computing"],["dc.bibliographiccitation.lastpage","117"],["dc.bibliographiccitation.volume","67"],["dc.contributor.author","Otto, F. C."],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Mueller, L."],["dc.date.accessioned","2018-11-07T09:30:36Z"],["dc.date.available","2018-11-07T09:30:36Z"],["dc.date.issued","2001"],["dc.description.abstract","We apply an iterative substructuring algorithm with transmission conditions of Robin-Robin type to the discretized Oseen problem appearing as a linearized variant of the incompressible Navier-Stokes equations. Here we consider finite element approximations using velocity/pressure pairs which satisfy the Babuska-Brezzi stability condition. After proving well-posedness and strong convergence of th method, we derive an a-posteriori error estimate which controls convergence of the discrete subdomain solutions to the global discrete solution by measuring the jumps of the velocities at the interface. Additionally we obtain information how to design a parameter of the Robin interface condition which essentially influences the convergence speed, Numerical experiments confirm the theoretical results and the applicability of the method."],["dc.identifier.doi","10.1007/s006070170009"],["dc.identifier.isi","000171142400001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/31343"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.publisher.place","Wien"],["dc.relation.issn","0010-485X"],["dc.title","An iterative substructuring method for div-stable finite element approximations of the Oseen problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","449"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","Numerical Linear Algebra with Applications"],["dc.bibliographiccitation.lastpage","472"],["dc.bibliographiccitation.volume","7"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Mueller, L."],["dc.contributor.author","Mueller, H."],["dc.date.accessioned","2018-11-07T10:32:16Z"],["dc.date.available","2018-11-07T10:32:16Z"],["dc.date.issued","2000"],["dc.description.abstract","We analyse a non-overlapping domain decomposition algorithm of Robin-Robin type applied to the discretized Oseen equations using stabilized finite element approximations of velocity/pressure thus allowing in particular equal-order interpolation. The new type of interface conditions takes advantage of the pressure regularization contained in the stabilized discrete problem. Finally we apply the method to the parallel solution of the nonstationary, incompressible Navier-Stokes equations. Some numerical results for standard benchmark problems are presented. Copyright (C) 2000 John Wiley & Sons, Ltd."],["dc.identifier.isi","000089169700005"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/44308"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Wiley-blackwell"],["dc.relation.issn","1070-5325"],["dc.title","A new non-overlapping domain decomposition method for stabilized finite element methods applied to the non-stationary Navier-Stokes equations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","49"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Computing"],["dc.bibliographiccitation.lastpage","68"],["dc.bibliographiccitation.volume","64"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Mueller, L."],["dc.contributor.author","Otto, F. C."],["dc.date.accessioned","2018-11-07T11:02:47Z"],["dc.date.available","2018-11-07T11:02:47Z"],["dc.date.issued","2000"],["dc.description.abstract","The application of a non-overlapping domain decomposition method to the solution of a stabilized finite element method for elliptic boundary value problems is considered. We derive an a-posteriori error estimate which bounds the error on the subdomains by the interface error of the subdomain solutions. As a by-product, some foundation is given to the design of the interface transmission condition. Numerical results support the theoretical results. Furthermore, we adapt a recent result on a-posteriori estimates for singular perturbation problems in order to obtain an a-posteriori estimate For the discrete subdomain solutions. AMS Subject Classifications: 65N55, 65N30."],["dc.identifier.doi","10.1007/s006070050003"],["dc.identifier.isi","000085727300003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/51468"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.publisher.place","Wien"],["dc.relation.issn","0010-485X"],["dc.title","A non-overlapping domain decomposition method for the advection-diffusion problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]