File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Convergence Rate For The Ordered Upwind Method

TitleConvergence Rate For The Ordered Upwind Method
Authors
KeywordsAnisotropic optimal control
Convergence rate
Error bound
Hamilton–Jacobi–Bellman equation
Ordered upwind methods
Viscosity solution
Issue Date2016
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474
Citation
Journal of Scientific Computing, 2016, v. 68, p. 889-913 How to Cite?
AbstractThe ordered upwind method (OUM) is used to approximate the viscosity solution of the static Hamilton---Jacobi---Bellman with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution that converges to the exact solution, but no convergence rate has been theoretically proven. In this paper, it is shown that the solutions produced by the OUM in the boundary value formulation converge at a rate of at least the square root of the largest edge length in the mesh in terms of maximum error. An example with similar order of numerical convergence is provided.
Persistent Identifierhttp://hdl.handle.net/10722/246528
ISSN
2023 Impact Factor: 2.8
2023 SCImago Journal Rankings: 1.248
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorShum, SA-
dc.contributor.authorMorris, K-
dc.contributor.authorKhajepour, A-
dc.date.accessioned2017-09-18T02:30:03Z-
dc.date.available2017-09-18T02:30:03Z-
dc.date.issued2016-
dc.identifier.citationJournal of Scientific Computing, 2016, v. 68, p. 889-913-
dc.identifier.issn0885-7474-
dc.identifier.urihttp://hdl.handle.net/10722/246528-
dc.description.abstractThe ordered upwind method (OUM) is used to approximate the viscosity solution of the static Hamilton---Jacobi---Bellman with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution that converges to the exact solution, but no convergence rate has been theoretically proven. In this paper, it is shown that the solutions produced by the OUM in the boundary value formulation converge at a rate of at least the square root of the largest edge length in the mesh in terms of maximum error. An example with similar order of numerical convergence is provided.-
dc.languageeng-
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474-
dc.relation.ispartofJournal of Scientific Computing-
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s10915-016-0163-3-
dc.subjectAnisotropic optimal control-
dc.subjectConvergence rate-
dc.subjectError bound-
dc.subjectHamilton–Jacobi–Bellman equation-
dc.subjectOrdered upwind methods-
dc.subjectViscosity solution-
dc.titleConvergence Rate For The Ordered Upwind Method-
dc.typeArticle-
dc.identifier.emailShum, SA: alexshum@hku.hk-
dc.description.naturepostprint-
dc.identifier.doi10.1007/s10915-016-0163-3-
dc.identifier.scopuseid_2-s2.0-84955257048-
dc.identifier.hkuros277666-
dc.identifier.volume68-
dc.identifier.spage889-
dc.identifier.epage913-
dc.identifier.isiWOS:000380693700001-
dc.publisher.placeUnited States-
dc.identifier.issnl0885-7474-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats