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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.03728 |
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| _version_ | 1866915141378899968 |
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| author | Lewis, T. Xue, X. |
| author_facet | Lewis, T. Xue, X. |
| contents | A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a high order correction to the Lax-Friedrich's method while utilizing a novel cutoff to preserve the convergence properties of the Lax-Friedrich's approximation. Since monotone methods are limited to first order accuracy by the Godunov barrier, the proposed approach provides a template for boosting the accuracy of a monotone method using a modified numerical moment stabilizer with a high-order auxiliary boundary condition. Numerical tests are provided to test the utility of the approach while a novel admissibility and stability analysis technique lays a foundation for analyzing non-monotone methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A high order correction to the Lax-Friedrich's method for approximating stationary Hamilton-Jacobi equations Lewis, T. Xue, X. Numerical Analysis 65N06, 65N12 A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a high order correction to the Lax-Friedrich's method while utilizing a novel cutoff to preserve the convergence properties of the Lax-Friedrich's approximation. Since monotone methods are limited to first order accuracy by the Godunov barrier, the proposed approach provides a template for boosting the accuracy of a monotone method using a modified numerical moment stabilizer with a high-order auxiliary boundary condition. Numerical tests are provided to test the utility of the approach while a novel admissibility and stability analysis technique lays a foundation for analyzing non-monotone methods. |
| title | A high order correction to the Lax-Friedrich's method for approximating stationary Hamilton-Jacobi equations |
| topic | Numerical Analysis 65N06, 65N12 |
| url | https://arxiv.org/abs/2502.03728 |