Some non monotone schemes for Hamilton-Jacobi-Bellman equations
We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete proble...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196520.pdf |
| _version_ | 1797965802389897216 |
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| author | Warin Xavier |
| author_facet | Warin Xavier |
| author_sort | Warin Xavier |
| collection | DOAJ |
| description | We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete problem can only be solved with some error. We give some examples of such numerical schemes and show that the bounds obtained by the framework developed are not tight. At last we test the schemes. |
| first_indexed | 2024-04-11T02:05:48Z |
| format | Article |
| id | doaj.art-0320d8896afa4a4890294748650a3f32 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:05:48Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-0320d8896afa4a4890294748650a3f322023-01-03T03:01:23ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592019-01-016547649710.1051/proc/201965476proc196520Some non monotone schemes for Hamilton-Jacobi-Bellman equationsWarin XavierWe extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete problem can only be solved with some error. We give some examples of such numerical schemes and show that the bounds obtained by the framework developed are not tight. At last we test the schemes.https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196520.pdf |
| spellingShingle | Warin Xavier Some non monotone schemes for Hamilton-Jacobi-Bellman equations ESAIM: Proceedings and Surveys |
| title | Some non monotone schemes for Hamilton-Jacobi-Bellman equations |
| title_full | Some non monotone schemes for Hamilton-Jacobi-Bellman equations |
| title_fullStr | Some non monotone schemes for Hamilton-Jacobi-Bellman equations |
| title_full_unstemmed | Some non monotone schemes for Hamilton-Jacobi-Bellman equations |
| title_short | Some non monotone schemes for Hamilton-Jacobi-Bellman equations |
| title_sort | some non monotone schemes for hamilton jacobi bellman equations |
| url | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196520.pdf |
| work_keys_str_mv | AT warinxavier somenonmonotoneschemesforhamiltonjacobibellmanequations |