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dc.contributor.authorHajduk, Hennes
dc.date.accessioned2020-07-23T09:35:43Z
dc.date.available2020-07-23T09:35:43Z
dc.date.issued2020-07-02
dc.identifier.urihttp://hdl.handle.net/10754/664384
dc.description.abstractIn this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well as hyperbolic systems. Our methodology for limiting volume terms is similar to recently proposed methods for continuous Galerkin approximations, while DG flux terms require novel stabilization techniques. Piecewise Bernstein polynomials are employed as shape functions for the DG spaces, thus facilitating the use of very high order spatial approximations. We discuss the design of a new, provably invariant domain preserving DG scheme that is then extended by state-of-the-art subcell flux limiters to obtain a high-order bound preserving approximation. The limiting procedures can be formulated in the semi-discrete setting. Thus convergence to steady state solutions is not inhibited by the algorithm. We present numerical results for a variety of benchmark problems. Conservation laws considered in this study are linear and nonlinear scalar problems, as well as the Euler equations of gas dynamics and the shallow water system.
dc.description.sponsorshipThe author would like to thank Prof. Dmitri Kuzmin (TU Dortmund University) for many insightful suggestions and supporting this effort in general. Special thanks go also to Dr. Manuel Quezada de Luna (King Abdullah University of Science and Technology) for many fruitful discussions.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2007.01212
dc.rightsArchived with thanks to arXiv
dc.titleMonolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
dc.typePreprint
dc.eprint.versionPre-print
dc.contributor.institutionInstitute of Applied Mathematics (LS III), TU Dortmund University, Vogelpothsweg 87, D-44227 Dortmund, Germany.
dc.identifier.arxivid2007.01212
refterms.dateFOA2020-07-23T09:36:28Z


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