Schröder, Philipp W.

[["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Journal of Numerical Mathematics"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2020-11-18T15:43:08Z"],["dc.date.available","2020-11-18T15:43:08Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1515/jnma-2016-1101"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68810"],["dc.relation.issn","1570-2820"],["dc.relation.issn","1569-3953"],["dc.title","Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier–Stokes flows"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","917"],["dc.bibliographiccitation.journal","Computers & Mathematics with Applications"],["dc.bibliographiccitation.lastpage","938"],["dc.bibliographiccitation.volume","341"],["dc.contributor.author","Akbas, Mine"],["dc.contributor.author","Linke, Alexander"],["dc.contributor.author","Rebholz, Leo G."],["dc.contributor.author","Schröder, Philipp W."],["dc.date.accessioned","2020-11-18T15:43:00Z"],["dc.date.available","2020-11-18T15:43:00Z"],["dc.date.issued","2017-11-13"],["dc.description.abstract","Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the relaxation of the divergence constraint in classical mixed methods, and are excited whenever the spatial discretization has to deal with comparably large and complicated pressures. In this contribution, an analogue of grad-div stabilization for Discontinuous Galerkin methods is studied. Here, the key is the penalization of the jumps of the normal velocities over facets of the triangulation, which controls the measure-valued part of the distributional divergence of the discrete velocity solution. Our contribution is twofold: first, we characterize the limit for arbitrarily large penalization parameters, which shows that the stabilized nonconforming Discontinuous Galerkin methods remain robust and accurate in this limit; second, we extend these ideas to the case of non-simplicial meshes; here, broken grad-div stabilization must be used in addition to the normal velocity jump penalization, in order to get the desired pressure robustness effect. The analysis is performed for the Stokes equations, and more complex flows and Crouzeix-Raviart elements are considered in numerical examples that also show the relevance of the theory in practical settings."],["dc.identifier.arxiv","1711.04442v3"],["dc.identifier.doi","10.1016/j.cma.2018.07.019"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68808"],["dc.relation.issn","0045-7825"],["dc.title","The analogue of grad-div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","533"],["dc.bibliographiccitation.issue","11"],["dc.bibliographiccitation.journal","International Journal for Numerical Methods in Fluids"],["dc.bibliographiccitation.lastpage","556"],["dc.bibliographiccitation.volume","91"],["dc.contributor.author","Fehn, Niklas"],["dc.contributor.author","Kronbichler, Martin"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schröder, Philipp W."],["dc.date.accessioned","2020-03-02T16:00:09Z"],["dc.date.available","2020-03-02T16:00:09Z"],["dc.date.issued","2019"],["dc.description.abstract","The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability are key ingredients to obtain robust and accurate discretisations. Recently, two approaches have been proposed in the context of high-order discontinuous Galerkin (DG) discretisations that address these aspects differently. On the one hand, standard ^2ehBbased DG discretisations enforce mass conservation and energy stability weakly by the use of additional stabilisation terms. On the other hand, pointwise divergence-free (\\operatorname{div})ehBconforming approaches ensure exact mass conservation and energy stability by the use of tailored finite element function spaces. The present work raises the question whether and to which extent these two approaches are equivalent when applied to under-resolved turbulent flows. This comparative study highlights similarities and differences of these two approaches. The numerical results emphasise that both discretisation strategies are promising for under-resolved simulations of turbulent flows due to their inherent dissipation mechanisms."],["dc.identifier.arxiv","1905.00142v1"],["dc.identifier.doi","10.1002/fld.4763"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63042"],["dc.language.iso","en"],["dc.notes.intern","DeepGreen Import"],["dc.relation.issn","0271-2091"],["dc.relation.issn","1097-0363"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","High-order DG solvers for under-resolved turbulent incompressible flows: A comparison of $L^2$ and $H(div)$ methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["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","1010"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Computers & Mathematics with Applications"],["dc.bibliographiccitation.lastpage","1028"],["dc.bibliographiccitation.volume","77"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","John, Volker"],["dc.contributor.author","Lederer, Philip L."],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schöberl, Joachim"],["dc.date.accessioned","2020-11-18T15:42:55Z"],["dc.date.available","2020-11-18T15:42:55Z"],["dc.date.issued","2018-03-19"],["dc.description.abstract","Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed."],["dc.identifier.arxiv","1803.06893v4"],["dc.identifier.doi","10.1016/j.camwa.2018.10.030"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68807"],["dc.relation.issn","0898-1221"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","830"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Scientific Computing"],["dc.bibliographiccitation.lastpage","858"],["dc.bibliographiccitation.volume","75"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2020-11-18T15:43:04Z"],["dc.date.available","2020-11-18T15:43:04Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1007/s10915-017-0561-1"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68809"],["dc.relation.issn","0885-7474"],["dc.relation.issn","1573-7691"],["dc.title","Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","760"],["dc.bibliographiccitation.journal","Journal of Computational Physics"],["dc.bibliographiccitation.lastpage","779"],["dc.bibliographiccitation.volume","335"],["dc.contributor.author","Schroeder, Philipp W."],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2018-11-07T10:24:59Z"],["dc.date.available","2018-11-07T10:24:59Z"],["dc.date.issued","2017"],["dc.description.abstract","This paper presents heavily grad-div and pressure jump stabilised, equal- and mixed order discontinuous Galerkin finite element methods for non -isothermal incompressible flows based on the Oberbeck-Boussinesq approximation. In this framework, the enthalpy porosity model for multiphase flow in melting and solidification problems can be employed. By considering the differentially heated cavity and the melting of pure gallium in a rectangular enclosure, it is shown that both boundary layers and sharp moving interior layers can be handled naturally by the proposed class of non-conforming methods. Due to the stabilising effect of the grad-div term and the robustness of discontinuous Galerkin methods, it is possible to solve the underlying problems accurately on coarse, non-adapted meshes. The interaction of heavy grad-div stabilisation and discontinuous Galerkin methods significantly improves the mass conservation properties and the overall accuracy of the numerical scheme which is observed for the first time. Hence, it is inferred that stabilised discontinuous Galerkin methods are highly robust as well as computationally efficient numerical methods to deal with natural convection problems arising in incompressible computational thermo-fluid dynamics. (C) 2017 Elsevier Inc. All rights reserved."],["dc.identifier.doi","10.1016/j.jcp.2017.01.055"],["dc.identifier.isi","000397072800034"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/42763"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Academic Press Inc Elsevier Science"],["dc.relation.issn","1090-2716"],["dc.relation.issn","0021-9991"],["dc.title","Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Proceedings in Applied Mathematics and Mechanics"],["dc.bibliographiccitation.volume","19"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schröder, Philipp W."],["dc.date.accessioned","2020-03-02T16:35:32Z"],["dc.date.available","2020-03-02T16:35:32Z"],["dc.date.issued","2019"],["dc.description.abstract","Nowadays, (high‐order) DG methods, or hybridised variants thereof, are widely used in the simulation of turbulent incompressible flow problems. For turbulence simulations, and especially in the practically relevant situation of strong under‐resolution, it is important to distinguish between the resolved physical dissipation rate and the contribution of numerical dissipation originating from the underlying method. In this note, a certain ambiguity related to such a decomposition for the viscous effects in a DG‐discretised fluid flow problem, which is due to the discontinuity of the approximate solution, is addressed. A novel but rather natural decomposition into ‘physical’ and ‘numerical’ viscous dissipation is proposed for a class of DG methods. Based on a typical 3D benchmark problem for decaying turbulence, its meaningfulness is confirmed numerically. In order to justify the term ‘dissipation’, both the physical and the numerical contributions for the proposed additive decomposition are provably non‐negative (possibly zero)."],["dc.identifier.doi","10.1002/pamm.201900049"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63061"],["dc.language.iso","en"],["dc.relation.issn","1617-7061"],["dc.relation.issn","1617-7061"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Viscous dissipation in DG methods for turbulent incompressible flows"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]