A second‐order isoparametric element method to solve plane linear elastic problem. Issue 2 (21st October 2020)

• Record Type: Journal Article
• Authors: Song, Shicang; Liu, Zhixin
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 2(2021)
• Page Start: 1535
• Page End: 1550
• Publication Date: 2020-10-21
• Subjects: error estimates -- isoparametric finite element -- numerical quadrature -- plane linear elastic problem; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22595
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: 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 function u ˜ → is an extension of the true solution u → to Ω ˜ . 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.