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C*‐convergence in the finite element method
Author(s) -
Bigdeli B.,
Kelly D. W.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19971215)40:23<4405::aid-nme267>3.0.co;2-k
Subject(s) - quadrilateral , finite element method , mathematics , mixed finite element method , degrees of freedom (physics and chemistry) , singularity , rate of convergence , elasticity (physics) , displacement (psychology) , convergence (economics) , mathematical analysis , extended finite element method , structural engineering , computer science , engineering , physics , economics , economic growth , psychology , computer network , channel (broadcasting) , quantum mechanics , psychotherapist , thermodynamics
In this paper a family of higher‐order quadrilaterals for the finite element analysis of plane elasticity problems are developed, using the displacement method formulation. The number of nodes and the number of elements are fixed, and refinement is achieved by adding derivatives of the nodal displacements as degrees of freedom at the nodes. It is shown that a higher rate of convergence is achieved compared with existing h ‐ and p ‐versions of the finite element method. Applications to stress concentration and stress singularity are presented and the condition number is checked. © 1997 John Wiley & Sons, Ltd.