Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913077161623552 |
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| author | Badal, Rufat Friedrich, Manuel Horák, Martin Kružík, Martin Machill, Lennart |
| author_facet | Badal, Rufat Friedrich, Manuel Horák, Martin Kružík, Martin Machill, Lennart |
| contents | We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kružík '23, Mielke-Roub\'ıček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_27923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations Badal, Rufat Friedrich, Manuel Horák, Martin Kružík, Martin Machill, Lennart Analysis of PDEs Numerical Analysis 35A15, 35Q74, 74A15, 74A30, 74D10, 74F05, 74G15, 74G22 We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kružík '23, Mielke-Roub\'ıček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically. |
| title | Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations |
| topic | Analysis of PDEs Numerical Analysis 35A15, 35Q74, 74A15, 74A30, 74D10, 74F05, 74G15, 74G22 |
| url | https://arxiv.org/abs/2604.27923 |