The second boundary value problem for a discrete Monge-Ampere equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866914863365750784 |
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| author | Awanou, Gerard |
| author_facet | Awanou, Gerard |
| contents | In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular Oliker-Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_14376 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The second boundary value problem for a discrete Monge-Ampere equation Awanou, Gerard Numerical Analysis 65N06, 52B55 In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular Oliker-Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given. |
| title | The second boundary value problem for a discrete Monge-Ampere equation |
| topic | Numerical Analysis 65N06, 52B55 |
| url | https://arxiv.org/abs/1910.14376 |