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An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems

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Listed:
  • Jue Qu

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
    Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China)

  • Hongjun Xue

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)

  • Yancheng Li

    (School of Naval Engineering, Wuxi Institute of Communications Technology, Wuxi 214151, China
    School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China)

  • Yingbin Chai

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China
    State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

A novel enriched finite element method (EFEM) was employed to analyze the transient wave propagation problems. In the present method, the traditional finite element approximation was enriched by employing the appropriate interpolation covers. We mathematically and numerically showed that the present EFEM possessed the important monotonic convergence property with the decrease of the used time steps for transient wave propagation problems when the unconditional stable Newmark time integration scheme was used for time integration. This attractive property markedly distinguishes the present EFEM from the traditional FEM for transient wave propagation problems. Two typical numerical examples were given to demonstrate the capabilities of the present method.

Suggested Citation

  • Jue Qu & Hongjun Xue & Yancheng Li & Yingbin Chai, 2022. "An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1380-:d:797848
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    References listed on IDEAS

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    1. Lin, Ji & Zhang, Yuhui & Reutskiy, Sergiy & Feng, Wenjie, 2021. "A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    2. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. You, Xiangyu & Li, Wei & Chai, Yingbin, 2020. "A truly meshfree method for solving acoustic problems using local weak form and radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    4. Wang, Fajie & Zhao, Qinghai & Chen, Zengtao & Fan, Chia-Ming, 2021. "Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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