Schröder, Philipp W.

[["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","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"]]