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A posteriori error estimates and adaptivity for finite element solutions in finite elasticity
Author(s) -
Mücke Roland,
Whiteman J. R.
Publication year - 1995
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.1620380505
Subject(s) - finite element method , estimator , discretization , elasticity (physics) , mathematics , mixed finite element method , a priori and a posteriori , linear elasticity , mathematical optimization , boundary value problem , convergence (economics) , mathematical analysis , statistics , philosophy , epistemology , economics , composite material , economic growth , physics , thermodynamics , materials science
Methods for a posteriori error estimation for finite element solutions are well established and widely used in engineering practice for linear boundary value problems. In contrast here we are concerned with finite elasticity and error estimation and adaptivity in this context. In the paper a brief outline of continuum theory of finite elasticity is first given. Using the residuals in the equilibrium conditions the discretization error of the finite element solution is estimated both locally and globally. The proposed error estimator is physically interpreted in the energy sense. We then present and discuss the convergence behaviour of the discretization error in uniformly and adaptively refined finite element sequences.