A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation: A dimension reduction method of two-grid finite element solution coefficient vectors for the Allen-Cahn equation
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| Titel: | A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation: A dimension reduction method of two-grid finite element solution coefficient vectors for the Allen-Cahn equation |
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| Autoren: | Yuejie Li, Fei Teng, Yihui Zeng, Zhendong Luo |
| Quelle: | Mathematical Methods in the Applied Sciences. 48:678-698 |
| Verlagsinformationen: | Wiley, 2024. |
| Publikationsjahr: | 2024 |
| Schlagwörter: | Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, two-grid Crank-Nicolson finite element method, unconditional stability and errors, Spectral, collocation and related methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, 0101 mathematics, nonlinear Allen-Cahn equation, 01 natural sciences, reduced-dimension extrapolated two-grid Crank-Nicolson finite element method |
| Beschreibung: | This paper mainly focuses on the dimension reduction of unknown finite element (FE) solution coefficient vectors in two‐grid Crank–Nicolson FE (TGCNFE) method for the nonlinear Allen–Cahn equation. For this purpose, a new TGCNFE method for the nonlinear Allen–Cahn equation is first developed and the unconditional stability and errors of TGCNFE solutions are analyzed. Thereafter, the most important thing is to lower the dimension of the unknown FE solution coefficient vectors by a proper orthogonal decomposition, to establish a new reduced‐dimension extrapolated TGCNFE (RDETGCNFE) method, and to analyze the unconditional stability and errors of RDETGCNFE solutions. Moreover, the correctness of our theoretical results is validated by some numerical experiments. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/xml |
| Sprache: | English |
| ISSN: | 1099-1476 0170-4214 |
| DOI: | 10.1002/mma.10350 |
| Rights: | Wiley Online Library User Agreement |
| Dokumentencode: | edsair.doi.dedup.....b83202da1d3f5a44b3822aa4b5026622 |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | This paper mainly focuses on the dimension reduction of unknown finite element (FE) solution coefficient vectors in two‐grid Crank–Nicolson FE (TGCNFE) method for the nonlinear Allen–Cahn equation. For this purpose, a new TGCNFE method for the nonlinear Allen–Cahn equation is first developed and the unconditional stability and errors of TGCNFE solutions are analyzed. Thereafter, the most important thing is to lower the dimension of the unknown FE solution coefficient vectors by a proper orthogonal decomposition, to establish a new reduced‐dimension extrapolated TGCNFE (RDETGCNFE) method, and to analyze the unconditional stability and errors of RDETGCNFE solutions. Moreover, the correctness of our theoretical results is validated by some numerical experiments. |
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| ISSN: | 10991476 01704214 |
| DOI: | 10.1002/mma.10350 |