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p ‐convergent finite element approximations in fracture mechanics
Author(s) -
Szabo B. A.,
Mehta A. K.
Publication year - 1978
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/nme.1620120313
Subject(s) - finite element method , polygon mesh , computation , mathematics , displacement (psychology) , mixed finite element method , extended finite element method , hp fem , constant (computer programming) , mathematical analysis , degrees of freedom (physics and chemistry) , geometry , finite element limit analysis , algorithm , physics , computer science , structural engineering , engineering , psychology , quantum mechanics , psychotherapist , programming language
The strain energy release rate ( G ) converges rapidly in finite element approximations in which the finite element mesh is fixed and the order of polynomial displacement interpolations ( p ) is increased. Numerical experiments indicate that the error in G is very closely estimated, even for small p and very coarse finite element meshes, by an expression of the form k (NDF) ‐1 in which k is a mesh dependent constant and NDF is the number of degrees‐of‐freedom. The method provides for very efficient and accurate computation of G without the use of special techniques.