Stability analysis of the free-surface Stokes problem and an unconditionally stable explicit scheme
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918056670789632 |
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| author | Tominec, Igor Lundgren, Lukas Löfgren, André Ahlkrona, Josefin |
| author_facet | Tominec, Igor Lundgren, Lukas Löfgren, André Ahlkrona, Josefin |
| contents | Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and conservation properties of the weak form of this system for Newtonian fluids and non-Newtonian fluids, at both the continuous and discrete levels. We perform the fully discrete stability analysis for finite element methods used in space with explicit and implicit Euler time-stepping methods used in time. Motivated by the theory, we propose a stabilization term designed for the explicit Euler discretization, which ensures unconditional time stability and permits conservation of the domain volume. Numerical experiments validate and support our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability analysis of the free-surface Stokes problem and an unconditionally stable explicit scheme Tominec, Igor Lundgren, Lukas Löfgren, André Ahlkrona, Josefin Numerical Analysis Analysis of PDEs 65J15, 65M12, 65M60 Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and conservation properties of the weak form of this system for Newtonian fluids and non-Newtonian fluids, at both the continuous and discrete levels. We perform the fully discrete stability analysis for finite element methods used in space with explicit and implicit Euler time-stepping methods used in time. Motivated by the theory, we propose a stabilization term designed for the explicit Euler discretization, which ensures unconditional time stability and permits conservation of the domain volume. Numerical experiments validate and support our theoretical findings. |
| title | Stability analysis of the free-surface Stokes problem and an unconditionally stable explicit scheme |
| topic | Numerical Analysis Analysis of PDEs 65J15, 65M12, 65M60 |
| url | https://arxiv.org/abs/2506.10447 |