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Bivariate Spline Finite Element Solver for Linear Hyperbolic Equations in Two-Dimensional Spaces

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Abstract

In this paper, a finite element method using bivariate spline on domains is proposed for solving linear hyperbolic equations in two-dimensional spaces. Bivariate spline space \(S_{4}^{2,3} (\Delta_{mn}^{(2)} )\) is constructed. It not only satisfies homogeneous boundary constraints but also satisfies interpolating boundary conditions on type-2 triangulations. Two examples are shown to confirm the correctness of theoretical conclusions. This means that spline method is efficient and feasible to solve 2D linear hyperbolic equations.

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Acknowledgements

The authors acknowledge the National Natural Science Foundation of China (Grant Nos. 11601056 and 51009017), the Fundamental Research Funds for the Central Universities (Grant Nos. 3132017055 and 3132016314), the National Scholarship Foundation of China.

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Authors and Affiliations

  1. College of Science, Dalian Maritime University, Dalian, China

    Kai Qu, Mengdi Zhang & Jiawei Xuan

  2. School of Marine Electrical Engineering, Dalian Maritime University, Dalian, China

    Ning Wang

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  1. Kai Qu
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  2. Mengdi Zhang
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  4. Jiawei Xuan
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Correspondence to Kai Qu.

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Qu, K., Zhang, M., Wang, N. et al. Bivariate Spline Finite Element Solver for Linear Hyperbolic Equations in Two-Dimensional Spaces. Wireless Pers Commun 102, 3067–3077 (2018). https://doi.org/10.1007/s11277-018-5326-0

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  • DOI: https://doi.org/10.1007/s11277-018-5326-0

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