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Article: Convergence Rate For The Ordered Upwind Method
| Title | Convergence Rate For The Ordered Upwind Method |
|---|---|
| Authors | |
| Keywords | Anisotropic optimal control Convergence rate Error bound Hamilton–Jacobi–Bellman equation Ordered upwind methods Viscosity solution |
| Issue Date | 2016 |
| Publisher | Springer 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? |
| Abstract | The 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 Identifier | http://hdl.handle.net/10722/246528 |
| ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 1.248 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Shum, SA | - |
| dc.contributor.author | Morris, K | - |
| dc.contributor.author | Khajepour, A | - |
| dc.date.accessioned | 2017-09-18T02:30:03Z | - |
| dc.date.available | 2017-09-18T02:30:03Z | - |
| dc.date.issued | 2016 | - |
| dc.identifier.citation | Journal of Scientific Computing, 2016, v. 68, p. 889-913 | - |
| dc.identifier.issn | 0885-7474 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/246528 | - |
| dc.description.abstract | The 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.language | eng | - |
| dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474 | - |
| dc.relation.ispartof | Journal of Scientific Computing | - |
| dc.rights | The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-016-0163-3 | - |
| dc.subject | Anisotropic optimal control | - |
| dc.subject | Convergence rate | - |
| dc.subject | Error bound | - |
| dc.subject | Hamilton–Jacobi–Bellman equation | - |
| dc.subject | Ordered upwind methods | - |
| dc.subject | Viscosity solution | - |
| dc.title | Convergence Rate For The Ordered Upwind Method | - |
| dc.type | Article | - |
| dc.identifier.email | Shum, SA: alexshum@hku.hk | - |
| dc.description.nature | postprint | - |
| dc.identifier.doi | 10.1007/s10915-016-0163-3 | - |
| dc.identifier.scopus | eid_2-s2.0-84955257048 | - |
| dc.identifier.hkuros | 277666 | - |
| dc.identifier.volume | 68 | - |
| dc.identifier.spage | 889 | - |
| dc.identifier.epage | 913 | - |
| dc.identifier.isi | WOS:000380693700001 | - |
| dc.publisher.place | United States | - |
| dc.identifier.issnl | 0885-7474 | - |