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

Jue Qu, Hongjun Xue, Yancheng Li and Yingbin Chai
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Jue Qu: School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, 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
Yingbin Chai: School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China

Mathematics, 2022, vol. 10, issue 9, 1-12

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.

Keywords: finite element; wave propagation analysis; numerical methods; dispersion analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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