Improved a priori error estimates for a space-time finite element method for parabolic problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910871819649024 |
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| author | Ta, Thi Thanh Mai Nguyen, Quang Huy Pham, Phi Hung |
| author_facet | Ta, Thi Thanh Mai Nguyen, Quang Huy Pham, Phi Hung |
| contents | In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved a priori error estimates for a space-time finite element method for parabolic problems Ta, Thi Thanh Mai Nguyen, Quang Huy Pham, Phi Hung Numerical Analysis 35K20, 65M15, 65M60 In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results. |
| title | Improved a priori error estimates for a space-time finite element method for parabolic problems |
| topic | Numerical Analysis 35K20, 65M15, 65M60 |
| url | https://arxiv.org/abs/2503.09229 |