scholarly journals Variational formulation of micropolar elasticity using 3D hexahedral finite-element interpolation with incompatible modes

2018 ◽  
Vol 205 ◽  
pp. 1-14 ◽  
Author(s):  
Sara Grbčić ◽  
Adnan Ibrahimbegović ◽  
Gordan Jelenić
Keyword(s):  
Finite Element ◽  
Variational Formulation ◽  
Micropolar Elasticity ◽  
Incompatible Modes

scholarly journals Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Yidu Yang ◽  
Yu Zhang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Adaptive Algorithm ◽  
Variational Formulation ◽  
High Efficiency ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.

Variational Formulation and Associated Algorithm for the Starved Finite Journal Bearing

1983 ◽  
Vol 105 (3) ◽  
pp. 453-457 ◽  
Author(s):  
G. Bayada
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Formulation ◽  
Flow Parameter ◽  
Journal Bearing ◽  
Numerical Treatment ◽  
Inlet Flow ◽  
Variational Form ◽  
Element Method

This paper is a contribution to the numerical treatment of the cavitation in a finite journal bearing when starvation takes place. A new variational form taking account the inlet flow parameter is given and allows us to compute rupture and reformation boundary together with the performances of the bearing via finite element method.

scholarly journals A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Yidu Yang ◽  
Wei Jiang ◽  
Yu Zhang ◽  
Wenjun Wang ◽  
Hai Bi
Keyword(s):  
Finite Element ◽  
Theoretical Analysis ◽  
Eigenvalue Problem ◽  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Discretization Scheme ◽  
Fine Grid ◽  
Asymptotically Optimal ◽  
Mixed Variational Formulation ◽  
Optimal Accuracy

This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems. With this scheme, the solution of an eigenvalue problem on a fine gridKhis reduced to the solution of an eigenvalue problem on a much coarser gridKHand the solution of a linear algebraic system on the fine gridKh. Theoretical analysis shows that the scheme has high efficiency. For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by takingH=O(h4), and when using thePk+1-Pkelement to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by takingH=O(h3). Finally, numerical experiments are presented to support the theoretical analysis.

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