$L^p$ Estimates for Numerical Approximation of Hamilton-Jacobi Equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915700704018432 |
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| author | Basti, Alessio Camilli, Fabio |
| author_facet | Basti, Alessio Camilli, Fabio |
| contents | We establish $L^p$ error estimates for monotone numerical schemes approximating Hamilton-Jacobi equations on the $d$-dimensional torus. Using the adjoint method, we first prove a $L^1$ error bound of order one for finite-difference and semi-Lagrangian schemes under standard convexity assumptions on the Hamiltonian. By interpolation, we also obtain $L^p$ estimates for every finite $p>1$. Our analysis covers a broad class of schemes, improves several existing results, and provides a unified framework for discrete error estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^p$ Estimates for Numerical Approximation of Hamilton-Jacobi Equations Basti, Alessio Camilli, Fabio Analysis of PDEs Numerical Analysis We establish $L^p$ error estimates for monotone numerical schemes approximating Hamilton-Jacobi equations on the $d$-dimensional torus. Using the adjoint method, we first prove a $L^1$ error bound of order one for finite-difference and semi-Lagrangian schemes under standard convexity assumptions on the Hamiltonian. By interpolation, we also obtain $L^p$ estimates for every finite $p>1$. Our analysis covers a broad class of schemes, improves several existing results, and provides a unified framework for discrete error estimates. |
| title | $L^p$ Estimates for Numerical Approximation of Hamilton-Jacobi Equations |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2512.24051 |