Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912160038256640 |
|---|---|
| author | Sun, Zhengjie Ling, Leevan Chen, Meng |
| author_facet | Sun, Zhengjie Ling, Leevan Chen, Meng |
| contents | In this paper, we propose a general meshless structure-preserving Galerkin method for solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and simulating the solution in the finite-dimensional approximation space spanned by (local) Lagrange functions generated with positive definite kernels, we obtain a semi-discrete Galerkin equation that inherits the energy dissipation property. The fully-discrete structure-preserving scheme is derived with the average vector field method. We provide a convergence analysis of the proposed method for the Allen-Cahn equation. The numerical experiments also verify the theoretical analysis including the convergence order and structure-preserving properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17478 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces Sun, Zhengjie Ling, Leevan Chen, Meng Numerical Analysis 65D05, 65M12, 65M60, 65N40 In this paper, we propose a general meshless structure-preserving Galerkin method for solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and simulating the solution in the finite-dimensional approximation space spanned by (local) Lagrange functions generated with positive definite kernels, we obtain a semi-discrete Galerkin equation that inherits the energy dissipation property. The fully-discrete structure-preserving scheme is derived with the average vector field method. We provide a convergence analysis of the proposed method for the Allen-Cahn equation. The numerical experiments also verify the theoretical analysis including the convergence order and structure-preserving properties. |
| title | Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces |
| topic | Numerical Analysis 65D05, 65M12, 65M60, 65N40 |
| url | https://arxiv.org/abs/2312.17478 |