Full metadata record
DC FieldValueLanguage
dc.contributor.authorKuzmin, Dmitri-
dc.description.abstractUsing the theoretical framework of algebraic flux correction and invariant domain preserving schemes, we introduce a monolithic approach to convex limiting in continuous finite element schemes for linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems. In contrast to fluxcorrected transport (FCT) algorithms that apply limited antidiffusive corrections to bound-preserving low-order solutions, our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions. Each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds. There is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately. Moreover, the steady-state limit of the nonlinear discrete problem is well defined and independent of the pseudo-time step. In the case study for the Euler equations, the components of the bar states are constrained sequentially to satisfy local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure. The results of numerical experiments for standard test problems illustrate the ability of built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner.de
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;609-
dc.subjecthyperbolic conservation lawsen
dc.subjectpositivity preservationen
dc.subjectinvariant domainen
dc.subjectfinite elementsen
dc.subjectalgebraic flux correctionen
dc.subjectconvex limitingen
dc.titleMonolithic convex limiting for continuous finite element discretizations of hyperbolic conservation lawsen
dcterms.accessRightsopen access-
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

Files in This Item:
File Description SizeFormat 
Ergebnisbericht Nr. 609.pdfDNB3.59 MBAdobe PDFView/Open

This item is protected by original copyright

Items in Eldorado are protected by copyright, with all rights reserved, unless otherwise indicated.