Error estimates for the Scaled Boundary Finite Element Method

被引:8
|
作者
Coelho, Karolinne O. [1 ]
Devloo, Philippe R. B. [1 ]
Gomes, Sonia M. [2 ]
机构
[1] Univ Estadual Campinas, FEC, R Josiah Willard Gibbs 85, BR-13083 Campinas, SP, Brazil
[2] Univ Estadual Campinas, IMECC, Campinas, SP, Brazil
基金
巴西圣保罗研究基金会;
关键词
Scaled boundary finite element method; A priori error estimates; Duffy's approximations; ISOPARAMETRIC ELEMENT; SINGULAR ELEMENT; ORDER;
D O I
10.1016/j.cma.2021.113765
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions, where the shape functions approximate local Dirichlet problems with piecewise polynomial trace data. Using this operator adaptation approach, and by imposing a starlike scaling requirement on the subregions, the representation of local SBFEM shape functions in radial and surface directions is obtained from eigenvalues and eigenfunctions of an ODE system, whose coefficients are determined by the element geometry and the trace polynomial spaces. The aim of this paper is to derive a priori error estimates for SBFEM's solutions of harmonic test problems. For that, the SBFEM spaces are characterized in the context of Duffy's approximations for which a gradient-orthogonality constraint is imposed. As a consequence, the scaled boundary functions are gradient-orthogonal to any function in Duffy's spaces vanishing at the mesh skeleton, a mimetic version of a well-known property valid for harmonic functions. This orthogonality property is applied to provide a priori SBFEM error estimates in terms of known finite element interpolant errors of the exact solution. Similarities with virtual harmonic approximations are also explored for the understanding of SBFEM convergence properties. Numerical experiments with 2D and 3D polytopal meshes confirm optimal SBFEM convergence rates for two test problems with smooth solutions. Attention is also paid to the approximation of a point singular solution by using SBFEM close to the singularity and finite element approximations elsewhere, revealing optimal accuracy rates of standard regular contexts. (C) 2021 Elsevier B.V. All rights reserved.
引用
收藏
页数:29
相关论文
共 50 条
  • [31] Approximative Green's Functions on Surfaces and Pointwise Error Estimates for the Finite Element Method
    Kroener, Heiko
    COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2017, 17 (01) : 51 - 64
  • [32] Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method
    林皋
    朱朝磊
    李建波
    胡志强
    Transactions of Tianjin University, 2013, (06) : 391 - 397
  • [33] Treatment of multiple input uncertainties using the scaled boundary finite element method
    Dsouza, Shaima M.
    Varghese, Tittu M.
    Ooi, Ean Tat
    Natarajan, Sundararajan
    Bordas, Stephane P. A.
    APPLIED MATHEMATICAL MODELLING, 2021, 99 : 538 - 554
  • [34] Dynamic crack propagation analysis using scaled boundary finite element method
    Lin G.
    Zhu C.
    Li J.
    Hu Z.
    Trans. Tianjin Univ., 2013, 6 (391-397): : 391 - 397
  • [35] A scaled boundary finite element method for static and dynamic analyses of cylindrical shells
    Li, Jianghuai
    Shi, Zhiyu
    Liu, Lei
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2019, 98 : 217 - 231
  • [36] Scaled Boundary Finite Element Method for Mid-Frequency Acoustics of Cavities
    Natarajan, Sundararajan
    Padmanabhan, Chandramouli
    JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS, 2021, 29 (01)
  • [37] Modelling dynamic crack propagation using the scaled boundary finite element method
    Ooi, E. T.
    Yang, Z. J.
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2011, 88 (04) : 329 - 349
  • [38] A p-hierarchical adaptive procedure for the scaled boundary finite element method
    Vu, Thu Hang
    Deeks, Andrew J.
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 73 (01) : 47 - 70
  • [39] Fracture analysis of piezoelectric materials using the scaled boundary finite element method
    Li, Chao
    Man, Hou
    Song, Chongmin
    Gao, Wei
    ENGINEERING FRACTURE MECHANICS, 2013, 97 : 52 - 71
  • [40] An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems
    Zhang ZiHua
    Yang ZhenJun
    Liu GuoHua
    Hu YunJin
    SCIENCE CHINA-TECHNOLOGICAL SCIENCES, 2011, 54 : 101 - 110