Implementation of non-conforming linear finite elements (Approximation APX5—Two-dimensional case)

2001 ◽  
pp. 321-335
Author(s):  
F. Thomasset
Keyword(s):  
Finite Elements ◽  
Dimensional Case ◽  
Two Dimensional

scholarly journals General polytopal H(div)-conformal finite elements and their discretisation spaces.

2020 ◽  
Author(s):  
Elise Le Meledo ◽  
Philipp Öffner ◽  
Remi Abgrall
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
General Setting ◽  
Basis Functions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wide Range ◽  
Virtual Element ◽  
Set Up

We present a class of discretisation spaces and H(div) - conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element's shape with the divergence properties of the Raviart - Thomas elements on the boundaries, the designed frameworks offer a wide range of H(div) - conformal discretisations. As those elements are set up through degrees of freedom, their definitions are easily amenable to the properties the approximated quantities are wished to fulfil. Furthermore, we show that one straightforward restriction of this general setting share its properties with the classical Raviart - Thomas elements at each interface, for any order and any polytopial shape. Then, to close the introduction of those new elements by an example, we investigate the shape of the basis functions corresponding to particular elements in the two dimensional case.

scholarly journals Solving the hourglass instability problem using rare mesh variation-difference schemes

2021 ◽  
Vol 2099 (1) ◽  
pp. 012003
Author(s):  
D T Chekmarev ◽  
Ya A Dawwas
Keyword(s):  
Finite Elements ◽  
High Efficiency ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Explicit Difference Scheme ◽  
Slow Convergence ◽  
Instability Problem ◽  
Instability Effect ◽  
2D And 3D

Abstract The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

Finite elements-boundary elements coupling for the movement modeling in two-dimensional structures

1992 ◽  
Vol 2 (11) ◽  
pp. 2035-2044 ◽  
Author(s):  
A. Nicolet ◽  
F. Delincé ◽  
A. Genon ◽  
W. Legros
Keyword(s):  
Finite Elements ◽  
Boundary Elements ◽  
Two Dimensional

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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