A deep first-order system least squares method for solving elliptic PDEs.
Resumen:
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and because of its meshless nature, it can also deal with problems posed in high-dimensional domains. We prove the Γ-convergence of the neural network approximation towards the solution of the continuous problem, and extend the convergence proof to some well-known related methods. Finally, we present several numerical examples illustrating the performance of our discretization.
| 2022 | |
| Francisco M. Bersetche ha sido financiado en parte por una beca postdoctoral de PEDECIBA y la beca ANPCyT PICT 2018-3017. | |
| Numerical Analysis | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47626 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
