Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation

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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Bibliographic Details
Main Authors: Yan Wang, Yining Yang, Nian Wang, Hong Li, Yang Liu
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Results in Applied Mathematics
Subjects:
Fractional hyperbolic wave model
Two-grid mixed finite element method
WSGD formula
Optimal error estimate
Online Access:http://www.sciencedirect.com/science/article/pii/S2590037424001006
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Summary: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.
ISSN:2590-0374

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