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A second‐order isoparametric element method to solve plane linear elastic problem
Author(s) -
Song Shicang,
Liu Zhixin
Publication year - 2021
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.22595
Subject(s) - mathematics , linear elasticity , finite element method , quadratic equation , isotropy , mathematical analysis , quadrature (astronomy) , boundary element method , boundary value problem , numerical analysis , elasticity (physics) , geometry , physics , materials science , quantum mechanics , electrical engineering , thermodynamics , engineering , composite material
Considering the both effect of boundary approximation and numerical quadrature, a second‐order isoparametric element method is given to solve the homogeneous isotropic plane linear elasticity problem in domain Ω with curved boundary. By using technically analysis, the optimal error estimate with ‖ u ˜ → − u → h ‖ 1 , Ω h= O ( h 2 )is obtained, where the functionu ˜ →is an extension of the true solutionu →toΩ ˜ . It yields better accuracy than traditional quadratic finite element method. Finally, two numerical examples are presented, which further illustrate the analytical result and show the scheme is effective.