The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain

2014 ◽  
Vol 30 (6) ◽  
pp. 1854-1876
Author(s):  
Wen-Ming He ◽  
Jun-Zhi Cui ◽  
Qi-Ding Zhu
Keyword(s):  
Triangular Element ◽  
Polygonal Domain ◽  
Poisson Problem ◽  
Local Superconvergence

Damping analysis of composite plates with zig-zag triangular element

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1211-1219
Author(s):  
D. G. Lee ◽  
J. B. Kosmatka
Keyword(s):  
Composite Plates ◽  
Triangular Element

Some Estimates for Virtual Element Methods

2017 ◽  
Vol 17 (4) ◽  
pp. 553-574 ◽  
Author(s):  
Susanne C. Brenner ◽  
Qingguang Guan ◽  
Li-Yeng Sung
Keyword(s):  
Error Estimates ◽  
Three Dimensions ◽  
Poisson Problem ◽  
Polyhedral Meshes ◽  
Virtual Element Methods ◽  
Virtual Element

AbstractWe present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Local A Posteriori Estimates on a Nonconvex Polygonal Domain

2012 ◽  
Vol 50 (2) ◽  
pp. 906-924 ◽  
Author(s):  
JaEun Ku ◽  
Alfred H. Schatz
Keyword(s):  
Polygonal Domain ◽  
A Posteriori ◽  
A Posteriori Estimates
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