Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909998419804160 |
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| author | Kopteva, Natalia Kelly, Sean |
| author_facet | Kopteva, Natalia Kelly, Sean |
| contents | Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^σ$ for any fixed $σ\in (0,1) \cup (1,2)$. The L1 scheme in time is combined with a general class of discretizations for the semilinear term. For such discretizations, we obtain sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading. Both semi-discretizations in time and full discretizations using finite differences and finite elements in space are addressed. The theoretcal findings are illustrated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes Kopteva, Natalia Kelly, Sean Numerical Analysis Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^σ$ for any fixed $σ\in (0,1) \cup (1,2)$. The L1 scheme in time is combined with a general class of discretizations for the semilinear term. For such discretizations, we obtain sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading. Both semi-discretizations in time and full discretizations using finite differences and finite elements in space are addressed. The theoretcal findings are illustrated by numerical experiments. |
| title | Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.12954 |