dc.date.accessioned | 2022-04-06T15:23:26Z | |
dc.date.available | 2022-04-06T15:23:26Z | |
dc.date.created | 2022-02-28T11:12:49Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Fjordholm, Ulrik Skre Ruf, Adrian Montgomery . Second-order accurate TVD numerical methods for nonlocal nonlinear conservation laws. SIAM Journal on Numerical Analysis. 2021, 59(3), 1167-1194 | |
dc.identifier.uri | http://hdl.handle.net/10852/93378 | |
dc.description.abstract | We present a second-order accurate numerical method for a class of nonlocal nonlinear conservation laws called the “nonlocal pair-interaction model,” which was recently introduced by Du, Huang, and LeFloch [SIAM J. Numer. Anal., 55 (2017), pp. 2465--2489]. Our numerical method uses second-order accurate reconstruction-based schemes for local conservation laws in conjunction with appropriate numerical integration. We show that the resulting method is total variation diminishing (TVD) and converges towards a weak solution. In fact, in contrast to local conservation laws, our second-order reconstruction-based method converges towards the unique entropy solution provided that the nonlocal interaction kernel satisfies a certain growth condition near zero. Furthermore, as the nonlocal horizon parameter in our method approaches zero we recover a well-known second-order method for local conservation laws. In addition, we answer several questions from the paper by Du, Huang, and LeFloch [SIAM J. Numer. Anal., 55 (2017), pp. 2465--2489] concerning regularity of solutions. In particular, we prove that any discontinuity present in a weak solution must be stationary and that if the interaction kernel satisfies a certain growth condition, then weak solutions are unique. We present a series of numerical experiments in which we investigate the accuracy of our second-order scheme, demonstrate shock formation in the nonlocal pair-interaction model, and examine how the regularity of the solution depends on the choice of flux function. | |
dc.language | EN | |
dc.title | Second-order accurate TVD numerical methods for nonlocal nonlinear conservation laws | |
dc.type | Journal article | |
dc.creator.author | Fjordholm, Ulrik Skre | |
dc.creator.author | Ruf, Adrian Montgomery | |
cristin.unitcode | 185,15,13,45 | |
cristin.unitname | Beregningsorientert matematikk | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 2006063 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM Journal on Numerical Analysis&rft.volume=59&rft.spage=1167&rft.date=2021 | |
dc.identifier.jtitle | SIAM Journal on Numerical Analysis | |
dc.identifier.volume | 59 | |
dc.identifier.issue | 3 | |
dc.identifier.startpage | 1167 | |
dc.identifier.endpage | 1194 | |
dc.identifier.doi | https://doi.org/10.1137/20M1360979 | |
dc.identifier.urn | URN:NBN:no-95950 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0036-1429 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/93378/1/nonlocalclaws.pdf | |
dc.type.version | AcceptedVersion | |