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On the TVD property of second order methods for 2D scalar conservation laws
dc.contributor.author | Krivodonova, Lilia | |
dc.contributor.author | Smirnov, Alexey | |
dc.date.accessioned | 2022-06-15 14:03:09 (GMT) | |
dc.date.available | 2022-06-15 14:03:09 (GMT) | |
dc.date.issued | 2021-10-05 | |
dc.identifier.uri | https://doi.org/10.48550/arXiv.2110.00067 | |
dc.identifier.uri | http://hdl.handle.net/10012/18378 | |
dc.description.abstract | The 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 definition | en |
dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada grant 341373-07 | en |
dc.language.iso | en | en |
dc.publisher | arXiv | en |
dc.subject | hyperbolic conservation laws | en |
dc.subject | total variation diminishing schemes | en |
dc.subject | discontinuous Galerkin method | en |
dc.subject | high-order methods | en |
dc.title | On the TVD property of second order methods for 2D scalar conservation laws | en |
dc.type | Preprint | en |
dcterms.bibliographicCitation | ArXiv.org e-Print archive. (n.d.). Retrieved June 14, 2022, from https://arxiv.org/ | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Applied Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Faculty | en |