Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913943549640704 |
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| author | Yuan, Hao Xie, Xiaoping |
| author_facet | Yuan, Hao Xie, Xiaoping |
| contents | This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type integro-differential equation and establish existence, uniqueness and regularity of its solution. Then we consider a conforming linear/bilinear/trilinear finite element semi-discrete scheme and a fast scheme of backward Euler full discretization with a sum-of-exponentials (SOE) approximation for the convolution integral, and derive error estimates for the semi-discrete and fully discrete schemes. Finally, we provide several numerical examples to verify the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation Yuan, Hao Xie, Xiaoping Numerical Analysis This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type integro-differential equation and establish existence, uniqueness and regularity of its solution. Then we consider a conforming linear/bilinear/trilinear finite element semi-discrete scheme and a fast scheme of backward Euler full discretization with a sum-of-exponentials (SOE) approximation for the convolution integral, and derive error estimates for the semi-discrete and fully discrete schemes. Finally, we provide several numerical examples to verify the theoretical results. |
| title | Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.11822 |