Quantum-assisted hλ-adaptive finite element method
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916488058765312 |
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| author | Drebotiy, R. H. Shynkarenko, H. A. |
| author_facet | Drebotiy, R. H. Shynkarenko, H. A. |
| contents | We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error control and corresponding approximation refinement. Appropriate finite element a posteriori error estimates are proved. Described approach demonstrates the possibility to overcome singular perturbations by applying error-controlled smoothening to finite element approximation. Possible benefits of the proposed finite element scheme are discussed and the numerical comparison with the typical adaptive scheme is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-assisted hλ-adaptive finite element method Drebotiy, R. H. Shynkarenko, H. A. Numerical Analysis We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error control and corresponding approximation refinement. Appropriate finite element a posteriori error estimates are proved. Described approach demonstrates the possibility to overcome singular perturbations by applying error-controlled smoothening to finite element approximation. Possible benefits of the proposed finite element scheme are discussed and the numerical comparison with the typical adaptive scheme is provided. |
| title | Quantum-assisted hλ-adaptive finite element method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.12687 |