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dc.contributor.authorKuzmin, Dmitri
dc.contributor.authorQuezada de Luna, Manuel
dc.date.accessioned2020-03-30T13:00:41Z
dc.date.available2020-03-30T13:00:41Z
dc.date.issued2020-03-21
dc.date.submitted2019-09-16
dc.identifier.citationKuzmin, D., & Quezada de Luna, M. (2020). Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws. Journal of Computational Physics, 411, 109411. doi:10.1016/j.jcp.2020.109411
dc.identifier.issn1090-2716
dc.identifier.issn0021-9991
dc.identifier.doi10.1016/j.jcp.2020.109411
dc.identifier.urihttp://hdl.handle.net/10754/662387
dc.description.abstractThis work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard Galerkin approximation is transformed into a nonlinear high-resolution scheme which has the compact sparsity pattern of the piecewise-linear or multilinear subcell discretization. The representation of this scheme in terms of invariant domain preserving states makes it possible to prove the validity of local discrete maximum principles under CFL-like conditions. In contrast to predictor-corrector approaches based on the flux-corrected transport methodology, the proposed flux limiting strategy is monolithic, i.e., limited antidiffusive terms are incorporated into the well-defined residual of a nonlinear (semi-)discrete problem. A stabilized high-order Galerkin discretization is recovered if no limiting is performed. In the limited version, the compact stencil property prevents direct mass exchange between nodes that are not nearest neighbors. A formal proof of sparsity is provided for simplicial and box elements. The involved element contributions can be calculated efficiently making use of matrix-free algorithms and precomputed element matrices of the reference element. Numerical studies for Q2 discretizations of linear and nonlinear two-dimensional test problems illustrate the virtues of monolithic convex limiting based on subcell flux decompositions.
dc.description.sponsorshipThe work of Dmitri Kuzmin was supported by the German Research Association (DFG) under grant KU 1530/23-1. The work of Manuel Quezada de Luna was supported by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. The authors would like to thank Prof. David I. Ketcheson (KAUST) and Christoph Lohmann (TU Dortmund University) for helpful discussions.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0021999120301856
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, [411, , (2020-03-21)] DOI: 10.1016/j.jcp.2020.109411 . © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleSubcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalJournal of Computational Physics
dc.eprint.versionPost-print
dc.contributor.institutionInstitute of Applied Mathematics (LS III), TU Dortmund University, Vogelpothsweg 87, D-44227 Dortmund, Germany
dc.identifier.volume411
dc.identifier.pages109411
dc.identifier.arxivid1909.03328
kaust.personQuezada de Luna, Manuel
dc.date.accepted2020-03-16
dc.identifier.eid2-s2.0-85082102015
refterms.dateFOA2020-03-31T09:00:43Z
dc.date.published-online2020-03-21
dc.date.published-print2020-06


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