scholarly journals Variational eigenvalue approximation of non-coercive operators with application to mixed formulations in elasticity

SeMA Journal ◽  
2022 ◽  
Author(s):  
Salim Meddahi
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Sufficient Conditions ◽  
Rates Of Convergence ◽  
Galerkin Scheme ◽  
Eigenvalue Approximation ◽  
Finite Element Approximations ◽  
Mixed Formulations ◽  
Optimal Rates Of Convergence ◽  
Abstract Framework

AbstractWe present an abstract framework for the eigenvalue approximation of a class of non-coercive operators. We provide sufficient conditions to guarantee the spectral correctness of the Galerkin scheme and to obtain optimal rates of convergence. The theory is applied to the convergence analysis of mixed finite element approximations of the elasticity and Stokes eigensystems.

Mixed Finite Element Models for Laminated Composite Plates

1987 ◽  
Vol 109 (1) ◽  
pp. 39-45 ◽  
Author(s):  
J. N. Reddy ◽  
D. Sandidge
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Accurate Determination ◽  
Mixed Finite Elements ◽  
Laminated Composite ◽  
Composite Plates ◽  
Finite Element Models ◽  
Finite Element Approximations ◽  
Mixed Formulations

Mixed finite element models of the classical and shear deformation plate theories are described, and their relative advantages, disadvantages and limitations are discussed. Numerical results showing the accuracy of the mixed finite elements are presented. Two main advantages of mixed models are the relaxation of continuity requirements on the interpolation functions and the accurate determination of the stress resultants. The disadvantages of mixed formulations are the difficulty in establishing convergence, accuracy and stability of finite element approximations and the computational expense.

A survey on mixed finite element approximations

1994 ◽  
Vol 30 (5) ◽  
pp. 3547-3551 ◽  
Author(s):  
F. Brezzi ◽  
D. Marini
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Finite Element Approximations

New Mixed Finite Element Formulations for Transient and Steady State Creep Problems

1989 ◽  
Vol 42 (11S) ◽  
pp. S150-S156
Author(s):  
Abimael F. D. Loula ◽  
Joa˜o Nisan C. Guerreiro
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Steady State Creep ◽  
Element Approximation ◽  
New Approach ◽  
Finite Element Approximations ◽  
Transient Problems ◽  
Transient And Steady State

We apply the mixed Petrov–Galerkin formulation to construct finite element approximations for transient and steady-state creep problems. With the new approach we recover stability, convergence, and accuracy of some Galerkin unstable approximations. We also present the main results on the numerical analysis and error estimates of the proposed finite element approximation for the steady problem, and discuss the asymptotic behavior of the continuum and discrete transient problems.

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