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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02277 |
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| _version_ | 1866910683719794688 |
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| author | Tripathi, Lok Pati Tomar, Aditi Pani, Amiya K. |
| author_facet | Tripathi, Lok Pati Tomar, Aditi Pani, Amiya K. |
| contents | A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time dependent coefficients and non-self-adjoint elliptic part. The proposed fully discrete method combines an IMEX-L1 method on a graded mesh in the temporal variable with a mixed finite element method in spatial variables. The focus of the study is to analyze stability results and to establish optimal error estimates, up to a logarithmic factor, for both the solution and the flux in $L^2$-norm when the initial data $u_0\in H_0^1(Ω)\cap H^2(Ω)$. Additionally, an error estimate in $L^\infty$-norm is derived for 2D problems. All the derived estimates and bounds in this article remain valid as $α\to 1^{-}$, where $α$ is the order of the Caputo fractional derivative. Finally, the results of several numerical experiments conducted at the end of this paper are confirming our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Non-Uniform $α$-Robust IMEX-L1 Mixed FEM for Time-Fractional PIDEs Tripathi, Lok Pati Tomar, Aditi Pani, Amiya K. Numerical Analysis A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time dependent coefficients and non-self-adjoint elliptic part. The proposed fully discrete method combines an IMEX-L1 method on a graded mesh in the temporal variable with a mixed finite element method in spatial variables. The focus of the study is to analyze stability results and to establish optimal error estimates, up to a logarithmic factor, for both the solution and the flux in $L^2$-norm when the initial data $u_0\in H_0^1(Ω)\cap H^2(Ω)$. Additionally, an error estimate in $L^\infty$-norm is derived for 2D problems. All the derived estimates and bounds in this article remain valid as $α\to 1^{-}$, where $α$ is the order of the Caputo fractional derivative. Finally, the results of several numerical experiments conducted at the end of this paper are confirming our theoretical findings. |
| title | On a Non-Uniform $α$-Robust IMEX-L1 Mixed FEM for Time-Fractional PIDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.02277 |