Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient
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| Format: | Preprint |
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2023
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| _version_ | 1866909583519252480 |
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| author | Płociniczak, Łukasz Taźbierski, Kacper |
| author_facet | Płociniczak, Łukasz Taźbierski, Kacper |
| contents | We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data and time-dependent diffusion coefficient. We prove the stability and convergence of the method under weak assumptions concerning regularity of the diffusivity. We find optimal pointwise in space and global in time errors, which are verified with several numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04246 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient Płociniczak, Łukasz Taźbierski, Kacper Numerical Analysis 65M12 G.1.8 We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data and time-dependent diffusion coefficient. We prove the stability and convergence of the method under weak assumptions concerning regularity of the diffusivity. We find optimal pointwise in space and global in time errors, which are verified with several numerical experiments. |
| title | Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient |
| topic | Numerical Analysis 65M12 G.1.8 |
| url | https://arxiv.org/abs/2310.04246 |