Lube, Gert

[["dc.bibliographiccitation.firstpage","437"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","IMA Journal of Numerical Analysis"],["dc.bibliographiccitation.lastpage","461"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Olshanskii, M. A."],["dc.date.accessioned","2018-11-07T10:21:17Z"],["dc.date.available","2018-11-07T10:21:17Z"],["dc.date.issued","2002"],["dc.description.abstract","Conforming finite-element approximations are considered for the incompressible Navier-Stokes equations with nonlinear terms written in the convection or rotation forms. Implicit time integration results in nice stability properties of auxiliary problems which can be solved by efficient numerical algorithms. The original nonlinear system admits relatively simple stabilization strategies. The paper presents in a unified form the convergence analysis, including the design of stabilization parameters, for linearized equations in both convection and rotation forms. Moreover, it is shown that a Galerkin discretization of the pressure-regularized Oseen problem with skew-symmetric terms in rotation form possesses better stability properties and, being much easier to solve, can be used as a predictor in implicit calculations."],["dc.identifier.doi","10.1093/imanum/22.3.437"],["dc.identifier.isi","000176605600006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/42056"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Oxford Univ Press"],["dc.relation.issn","0272-4979"],["dc.title","Stable finite-element calculation of incompressible flows using the rotation form of convection"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["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","116"],["dc.bibliographiccitation.issue","2-3"],["dc.bibliographiccitation.journal","Journal of Computational Mathematics"],["dc.bibliographiccitation.lastpage","147"],["dc.bibliographiccitation.volume","27"],["dc.contributor.author","Braack, Malte"],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2018-11-07T08:32:15Z"],["dc.date.available","2018-11-07T08:32:15Z"],["dc.date.issued","2009"],["dc.description.abstract","In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization (LPS). These methods preserve the favourable stability and approximation properties of classical residual-based stabilization (RBS) techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the Navier-Stokes equations. Furthermore, we apply it to optimal control problems with linear(ized) How problems, since the symmetry of the stabilization leads to the nice feature that the operations \"discretize\" and \"optimize\" commute."],["dc.identifier.isi","000265073400002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/17294"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Global Science Press"],["dc.publisher.place","Wanchai"],["dc.relation.conference","2nd Sino-German Workshop on Computational and Applied Mathematics"],["dc.relation.eventlocation","Hangzhou, PEOPLES R CHINA"],["dc.relation.issn","1991-7139"],["dc.relation.issn","0254-9409"],["dc.title","FINITE ELEMENTS WITH LOCAL PROJECTION STABILIZATION FOR INCOMPRESSIBLE FLOW PROBLEMS"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","629"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","SeMA Journal"],["dc.bibliographiccitation.lastpage","653"],["dc.bibliographiccitation.volume","75"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Linke, Alexander"],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2020-03-02T16:11:38Z"],["dc.date.available","2020-03-02T16:11:38Z"],["dc.date.issued","2018"],["dc.description.abstract","Inf-sup stable FEM applied to time-dependent incompressible Navier–Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure–robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Re-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on the essential regularity assumption ∇u∈L1(0,T;L∞(Ω)) which is discussed in detail. In the sense of best practice, we review and establish pressure- and Re-semi-robust estimates for pointwise divergence-free H1-conforming FEM (like Scott–Vogelius pairs or certain isogeometric based FEM) and pointwise divergence-free H(div)-conforming discontinuous Galerkin FEM. For convection-dominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradient-based."],["dc.identifier.doi","10.1007/s40324-018-0157-1"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63048"],["dc.language.iso","en"],["dc.relation.issn","2254-3902"],["dc.relation.issn","2281-7875"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2484"],["dc.bibliographiccitation.issue","16"],["dc.bibliographiccitation.journal","Mathematical Methods in the Applied Sciences"],["dc.bibliographiccitation.lastpage","2501"],["dc.bibliographiccitation.volume","37"],["dc.contributor.author","Lemster, W."],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Of, G."],["dc.contributor.author","Steinbach, O."],["dc.date.accessioned","2018-11-07T09:32:38Z"],["dc.date.available","2018-11-07T09:32:38Z"],["dc.date.issued","2014"],["dc.description.abstract","We consider a kinematic dynamo model in a bounded interior simply connected region Omega and in an insulating exterior region Omega(c) := R-3(Omega) over bar. In the so-called direct problem, the magnetic field B and the electric field E are unknown and are driven by a given incompressible flow field w. After eliminating E, a vector and a scalar potential ansatz for B in the interior and exterior domains, respectively, are applied, leading to a coupled interface problem. We apply a finite element approach in the bounded interior domain Omega, whereas a symmetric boundary element approach in the unbounded exterior domain Omega(c) is used. We present results on the well-posedness of the continuous coupled variational formulation, prove the well-posedness and stability of the semi-discretized and fully discretized schemes, and provide quasi-optimal error estimates for the fully discretized scheme. Copyright (C) 2013 John Wiley & Sons, Ltd."],["dc.identifier.doi","10.1002/mma.2991"],["dc.identifier.isi","000343835100011"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/31793"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Wiley-blackwell"],["dc.relation.issn","1099-1476"],["dc.relation.issn","0170-4214"],["dc.title","Analysis of a kinematic dynamo model with FEM-BEM coupling"],["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","1527"],["dc.bibliographiccitation.issue","12"],["dc.bibliographiccitation.journal","International Journal for Numerical Methods in Fluids"],["dc.bibliographiccitation.lastpage","1538"],["dc.bibliographiccitation.volume","40"],["dc.contributor.author","Knopp, Tobias"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Gritzki, Ralf"],["dc.contributor.author","Rosler, M."],["dc.date.accessioned","2018-11-07T09:41:21Z"],["dc.date.available","2018-11-07T09:41:21Z"],["dc.date.issued","2002"],["dc.description.abstract","The parallel solution of the incompressible Navier-Stokes equations coupled with the energy equation is considered. For turbulent flows, the k/epsilon model together with a modified wall-function concept is used. The iterative process requires the fast solution of advection-diffusion reaction and Oseen-type problems. These linearized problems are discretized using stabilized finite element methods. We apply a coarse-granular iterative substructuring method which couples the subdomain problems via Robin-type interface conditions. Then we apply the approach to the simulation of indoor air flow problems. Copyright (C) 2002 John Wiley Sons, Ltd."],["dc.identifier.doi","10.1002/fld.409"],["dc.identifier.isi","000179931400007"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33709"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","John Wiley & Sons Ltd"],["dc.publisher.place","W sussex"],["dc.relation.conference","Workshop on Domain Decomposition Methods in Fluid Mechanics"],["dc.relation.eventlocation","UNIV GREENWICH, LONDON, ENGLAND"],["dc.relation.issn","0271-2091"],["dc.title","Iterative substructuring methods for incompressible non-isothermal flows and its application to indoor air flow simulation"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","243"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Computational and Applied Mathematics"],["dc.bibliographiccitation.lastpage","267"],["dc.bibliographiccitation.volume","177"],["dc.contributor.author","Gelhard, T."],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Olshanskii, M. A."],["dc.contributor.author","Starcke, J. H."],["dc.date.accessioned","2018-11-07T11:00:36Z"],["dc.date.available","2018-11-07T11:00:36Z"],["dc.date.issued","2005"],["dc.description.abstract","We study stabilized FE approximations of SUPG type to the incompressible Navier-Stokes problem. Revisiting the analysis for the linearized model, we show that for conforming LBB-stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal-order approximation. Then we analyze a reduced SUPG scheme often used in practice for LBB-stable elements. To provide the reduced scheme with appropriate stability estimates we introduce a modified LBB condition which is proved for a family of FE approximations. The analysis is given for the linearized equations. Numerical experiments for some linear and nonlinear benchmark problems support the theoretical results. (C) 2004 Elsevier B.V. All rights reserved."],["dc.identifier.doi","10.1016/j.cam.2004.09.017"],["dc.identifier.isi","000227509200002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50959"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.relation.issn","0377-0427"],["dc.title","Stabilized finite element schemes with LBB-stable elements for incompressible flows"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","1150011"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Mathematical Models and Methods in Applied Sciences"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Loewe, Johannes"],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2018-11-07T09:14:11Z"],["dc.date.available","2018-11-07T09:14:11Z"],["dc.date.issued","2012"],["dc.description.abstract","We consider a projection-based variational multiscale method for large-eddy simulation of the Navier-Stokes/Fourier model of incompressible, non-isothermal flows. For the semidiscrete problem, an a priori error estimate is given for rather general nonlinear, piecewise constant coefficients of the subgrid models for the unresolved scales of velocity, pressure, and temperature. Then we address aspects of the discretization in time. Finally, the design of the subgrid scale models is specified for the case of free convection problems and studied for the standard benchmark problem of free convection in a closed cavity."],["dc.identifier.doi","10.1142/S0218202511500114"],["dc.identifier.isi","000300793600006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/27346"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","World Scientific Publ Co Pte Ltd"],["dc.relation.issn","1793-6314"],["dc.relation.issn","0218-2025"],["dc.title","A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1551"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","International Journal of Computer Mathematics"],["dc.bibliographiccitation.lastpage","1562"],["dc.bibliographiccitation.volume","85"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Knopp, Tobias"],["dc.contributor.author","Gritzki, Ralf"],["dc.contributor.author","Roesler, M."],["dc.contributor.author","Seifert, J."],["dc.date.accessioned","2018-11-07T11:20:06Z"],["dc.date.available","2018-11-07T11:20:06Z"],["dc.date.issued","2008"],["dc.description.abstract","A framework for solving the non-isothermal unsteady Reynolds-averaged Navier-Stokes equations with emphasis on applications to thermal building simulation is prescribed in this paper. Different domain decomposition techniques are used (i) for the treatment of boundary layers, (ii) for the efficient solution of the arising linear subproblems, and (iii) for coupling the indoor air flow field with the ambient. The approach is then applied to exemplary indoor air flow configurations."],["dc.identifier.doi","10.1080/00207160802033541"],["dc.identifier.isi","000258450800006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55456"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Taylor & Francis Ltd"],["dc.publisher.place","Abingdon"],["dc.relation.conference","Japan-France Conference on Analytical and Numerical Methods for Scientific Computing in Science and Engineering"],["dc.relation.eventlocation","Univ Henri Poincare, Nancy, FRANCE"],["dc.relation.issn","0020-7160"],["dc.title","Application of domain decomposition methods to indoor air flow simulation"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]