On the TVD property of second order methods for 2D scalar conservation laws

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dc.contributor.authorKrivodonova, Lilia
dc.contributor.authorSmirnov, Alexey
dc.date.accessioned2022-06-15T14:03:09Z
dc.date.available2022-06-15T14:03:09Z
dc.date.issued2021-10-05
dc.description.abstractThe total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in [14] that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definitionen
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada grant 341373-07en
dc.identifier.urihttps://doi.org/10.48550/arXiv.2110.00067
dc.identifier.urihttp://hdl.handle.net/10012/18378
dc.language.isoenen
dc.publisherarXiven
dc.subjecthyperbolic conservation lawsen
dc.subjecttotal variation diminishing schemesen
dc.subjectdiscontinuous Galerkin methoden
dc.subjecthigh-order methodsen
dc.titleOn the TVD property of second order methods for 2D scalar conservation lawsen
dc.typePreprinten
dcterms.bibliographicCitationArXiv.org e-Print archive. (n.d.). Retrieved June 14, 2022, from https://arxiv.org/en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Applied Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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