Space-time adaptive methods for parabolic evolution equations
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866912731786903552 |
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| author | Wang, Jun Su, Jie Greengard, Leslie Jiang, Shidong Veerapaneni, Shravan |
| author_facet | Wang, Jun Su, Jie Greengard, Leslie Jiang, Shidong Veerapaneni, Shravan |
| contents | We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the development of methods that can efficiently follow complex solution features in space-time by refinement and coarsening at each time step on an adaptive quadtree. For simplicity, we focus on problems posed in a square domain with periodic boundary conditions. The performance and robustness of the methods are illustrated with several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space-time adaptive methods for parabolic evolution equations Wang, Jun Su, Jie Greengard, Leslie Jiang, Shidong Veerapaneni, Shravan Numerical Analysis 65M80, 65M50, 35K05, 35K57, 35K91, 76D05, 31A10, 65F30, 65E05, 65Y20 We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the development of methods that can efficiently follow complex solution features in space-time by refinement and coarsening at each time step on an adaptive quadtree. For simplicity, we focus on problems posed in a square domain with periodic boundary conditions. The performance and robustness of the methods are illustrated with several numerical examples. |
| title | Space-time adaptive methods for parabolic evolution equations |
| topic | Numerical Analysis 65M80, 65M50, 35K05, 35K57, 35K91, 76D05, 31A10, 65F30, 65E05, 65Y20 |
| url | https://arxiv.org/abs/2511.18180 |