A new analytical technique of the fully implicit Crank-Nicolson discontinuous Galerkin method for the Ginzburg-Landau Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908676744282112 |
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| author | Cao, Xianxian Guan, Zhen Wang, Junjun |
| author_facet | Cao, Xianxian Guan, Zhen Wang, Junjun |
| contents | In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed numerical scheme, as well as its unconditionally optimal error estimates under both the \(L^2\)-norm and the energy norm. The core of the proof hinges on the \(L^2\)-norm boundedness of the numerical solution and the refined estimation of the cubic nonlinear term. Finally, two numerical examples are presented to validate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new analytical technique of the fully implicit Crank-Nicolson discontinuous Galerkin method for the Ginzburg-Landau Model Cao, Xianxian Guan, Zhen Wang, Junjun Numerical Analysis In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed numerical scheme, as well as its unconditionally optimal error estimates under both the \(L^2\)-norm and the energy norm. The core of the proof hinges on the \(L^2\)-norm boundedness of the numerical solution and the refined estimation of the cubic nonlinear term. Finally, two numerical examples are presented to validate the theoretical findings. |
| title | A new analytical technique of the fully implicit Crank-Nicolson discontinuous Galerkin method for the Ginzburg-Landau Model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.21168 |