Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation
In this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter θ is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD)...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424001006 |
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| author | Yan Wang Yining Yang Nian Wang Hong Li Yang Liu |
| author_facet | Yan Wang Yining Yang Nian Wang Hong Li Yang Liu |
| author_sort | Yan Wang |
| collection | DOAJ |
| description | In this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter θ is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD) formula is used to approximate the fractional time derivative at time tn−θ, and the spatial direction is approximated by a two-grid H1-Galerkin MFE method. The error estimates in both L2 and H1-norm for the fully discrete T-GMFE system are proved. Further, a modified T-GMFE scheme is proposed and the optimal error results are provided. Finally, computing results show the presented T-GMFE method can save computing time and improve the computational efficiency. |
| format | Article |
| id | doaj-art-08b03e9f5cc54af49edc27bba6aaa114 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-08b03e9f5cc54af49edc27bba6aaa1142025-08-20T02:47:33ZengElsevierResults in Applied Mathematics2590-03742025-02-012510053010.1016/j.rinam.2024.100530Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equationYan Wang0Yining Yang1Nian Wang2Hong Li3Yang Liu4School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, ChinaCorresponding author.; School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, ChinaIn this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter θ is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD) formula is used to approximate the fractional time derivative at time tn−θ, and the spatial direction is approximated by a two-grid H1-Galerkin MFE method. The error estimates in both L2 and H1-norm for the fully discrete T-GMFE system are proved. Further, a modified T-GMFE scheme is proposed and the optimal error results are provided. Finally, computing results show the presented T-GMFE method can save computing time and improve the computational efficiency.http://www.sciencedirect.com/science/article/pii/S2590037424001006Fractional hyperbolic wave modelTwo-grid mixed finite element methodWSGD formulaOptimal error estimate |
| spellingShingle | Yan Wang Yining Yang Nian Wang Hong Li Yang Liu Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation Results in Applied Mathematics Fractional hyperbolic wave model Two-grid mixed finite element method WSGD formula Optimal error estimate |
| title | Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation |
| title_full | Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation |
| title_fullStr | Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation |
| title_full_unstemmed | Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation |
| title_short | Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation |
| title_sort | two grid mixed finite element method combined with the bdf2 θ for a two dimensional nonlinear fractional pseudo hyperbolic wave equation |
| topic | Fractional hyperbolic wave model Two-grid mixed finite element method WSGD formula Optimal error estimate |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424001006 |
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