Structure-preserving scheme for 1D KWC system
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908414914854912 |
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| author | Okumura, Makoto Kubota, Shodai Shirakawa, Ken |
| author_facet | Okumura, Makoto Kubota, Shodai Shirakawa, Ken |
| contents | In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is that the equation for the crystalline orientation angle is described as a quasilinear diffusion equation with variable mobility. The goal of this paper is to establish a structure-preserving numerical scheme for the system, focusing on two main structural properties: $\sharp\,1)$ range preservation; and $\sharp\,2)$ energy dissipation. Under suitable assumptions, we construct a structure-preserving numerical scheme and address the following in the main theorems: (O) verification of the structural properties; (I) clarification of the convergence conditions; and (II) error estimate for the scheme. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_16963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-preserving scheme for 1D KWC system Okumura, Makoto Kubota, Shodai Shirakawa, Ken Numerical Analysis 35A15, 35K20, 65M12, 65M06, 74N20 In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is that the equation for the crystalline orientation angle is described as a quasilinear diffusion equation with variable mobility. The goal of this paper is to establish a structure-preserving numerical scheme for the system, focusing on two main structural properties: $\sharp\,1)$ range preservation; and $\sharp\,2)$ energy dissipation. Under suitable assumptions, we construct a structure-preserving numerical scheme and address the following in the main theorems: (O) verification of the structural properties; (I) clarification of the convergence conditions; and (II) error estimate for the scheme. |
| title | Structure-preserving scheme for 1D KWC system |
| topic | Numerical Analysis 35A15, 35K20, 65M12, 65M06, 74N20 |
| url | https://arxiv.org/abs/2506.16963 |