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High‐order dual‐parametric finite element methods for cavitation computation in nonlinear elasticity
Author(s) -
Huang Weijie,
Ma Weijun,
Wei Liang,
Li Zhiping
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22462
Subject(s) - finite element method , parametric statistics , mathematics , numerical analysis , computation , gaussian quadrature , nonlinear system , mixed finite element method , extended finite element method , smoothed finite element method , mathematical analysis , gaussian , quadrature (astronomy) , boundary knot method , algorithm , structural engineering , physics , nyström method , integral equation , engineering , statistics , quantum mechanics , optics , boundary element method
In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected.