A difference analog of the korn inequality

1989 ◽  
Vol 46 (6) ◽  
pp. 2176-2182 ◽  
Author(s):  
V. D. Glushenkov
Keyword(s):  
Difference Analog ◽  
Korn Inequality

scholarly journals A nonlinear Korn inequality in $\protect \mathbb{R}^n$ with an explicitly bounded constant

2020 ◽  
Vol 358 (5) ◽  
pp. 621-626
Author(s):  
Maria Malin ◽  
Cristinel Mardare
Keyword(s):  
Korn Inequality

scholarly journals Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

2017 ◽  
Vol 224 (3) ◽  
pp. 1205-1236 ◽  
Author(s):  
Jun Geng ◽  
Zhongwei Shen ◽  
Liang Song
Keyword(s):  
Neumann Problems ◽  
Korn Inequality

scholarly journals A Nonlinear Korn Inequality Based on the Green-Saint Venant Strain Tensor

2016 ◽  
Vol 126 (1) ◽  
pp. 129-134
Author(s):  
Alessandro Musesti
Keyword(s):  
Strain Tensor ◽  
Korn Inequality

Jackson-type integrals, bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system

1992 ◽  
Vol 26 (3) ◽  
pp. 153-165 ◽  
Author(s):  
N. Reshetikhin
Keyword(s):  
Jackson Type ◽  
Difference Analog

Two low-order nonconforming finite element methods for the Stokes flow in three dimensions

2018 ◽  
Vol 39 (3) ◽  
pp. 1447-1470 ◽  
Author(s):  
Jun Hu ◽  
Mira Schedensack
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stokes Flow ◽  
Three Dimensions ◽  
Nonconforming Finite Element ◽  
Discrete Problem ◽  
Piecewise Affine ◽  
Korn Inequality ◽  
Nonconforming Finite Element Methods ◽  
Low Order

Abstract In this paper, we propose two low-order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the nonconforming FEM of Kouhia & Stenberg (1995, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Eng, 124, 195–212). The finite element spaces proposed in this paper consist of two globally continuous components (one piecewise affine and one enriched component) and one component that is continuous at the midpoints of interior faces. We prove that the discrete Korn inequality and a discrete inf–sup condition hold uniformly in the mesh size and also for a nonempty Neumann boundary. Based on these two results, we show the well-posedness of the discrete problem. Two counterexamples prove that there is no direct generalization of the Kouhia–Stenberg FEM to three space dimensions: the finite element space with one nonconforming and two conforming piecewise affine components does not satisfy a discrete inf–sup condition with piecewise constant pressure approximations, while finite element functions with two nonconforming and one conforming component do not satisfy a discrete Korn inequality.

Integrability, Fusion, and Duality in the Elliptic Ruijsenaars Model

1997 ◽  
Vol 12 (11) ◽  
pp. 751-761 ◽  
Author(s):  
Kazuhiro Hikami ◽  
Yasushi Komori
Keyword(s):  
Difference Operator ◽  
Hecke Algebra ◽  
Root Systems ◽  
Baxter Equation ◽  
Reflection Equation ◽  
Fusion Procedure ◽  
Affine Hecke Algebra ◽  
Difference Analog ◽  
Type D ◽  
Ruijsenaars Models

The generalized elliptic Ruijsenaars models, which are regarded as a difference analog of the Calogero–Sutherland–Moser models associated with the classical root systems are studied. The integrability and the duality using the fusion procedure of operator-valued solutions of the Yang–Baxter equation and the reflection equation are shown. In particular a new integrable difference operator of type-D is proposed. The trigonometric models are also considered in terms of the representation of the affine Hecke algebra.

Korn Inequality for a Thin Periodic Corrugated Beam

2017 ◽  
Vol 226 (4) ◽  
pp. 375-387
Author(s):  
G. Leugering ◽  
S. A. Nazarov ◽  
A. S. Slutskii
Keyword(s):  
Korn Inequality ◽  
Corrugated Beam
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