New mixed finite elements for plane elasticity and Stokes equations

2011 ◽  
Vol 54 (7) ◽  
pp. 1499-1519 ◽  
Author(s):  
XiaoPing Xie ◽  
JinChao Xu
Keyword(s):  
Finite Elements ◽  
Stokes Equations ◽  
Mixed Finite Elements ◽  
Plane Elasticity

Stabilization of Low-order Mixed Finite Elements for the Stokes Equations

2006 ◽  
Vol 44 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Pavel B. Bochev ◽  
Clark R. Dohrmann ◽  
Max D. Gunzburger
Keyword(s):  
Finite Elements ◽  
Stokes Equations ◽  
Mixed Finite Elements ◽  
Low Order

scholarly journals RECTANGULAR MIXED FINITE ELEMENTS FOR ELASTICITY

2005 ◽  
Vol 15 (09) ◽  
pp. 1417-1429 ◽  
Author(s):  
DOUGLAS N. ARNOLD ◽  
GERARD AWANOU
Keyword(s):  
Finite Elements ◽  
Vector Fields ◽  
Mixed Finite Elements ◽  
Symmetric Tensor ◽  
Plane Elasticity ◽  
Discrete Version ◽  
Tensor Fields ◽  
Piecewise Polynomials ◽  
The Family ◽  
Differential Complex

We present a family of stable rectangular mixed finite elements for plane elasticity. Each member of the family consists of a space of piecewise polynomials discretizing the space of symmetric tensor fields in which the stress field is sought, and another to discretize the space of vector fields in which the displacement is sought. These may be viewed as analogues in the case of rectangular meshes of mixed finite elements recently proposed for triangular meshes. As for the triangular case the elements are closely related to a discrete version of the elasticity differential complex.

A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier–Stokes equations

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Alexander Linke ◽  
Michael Neilan ◽  
Leo G. Rebholz ◽  
Nicholas E. Wilson
Keyword(s):  
Finite Elements ◽  
Stokes Equations ◽  
Mixed Finite Elements ◽  
Projection Methods ◽  
Navier Stokes ◽  
Spatial Discretization ◽  
Navier Stokes Equations ◽  
Coupled Method

AbstractWe prove that for several inf-sup stable mixed finite elements, the solution of the Chorin/Temam projection methods for Navier–Stokes equations equipped with grad–div stabilization with parameter γ converge to the associated coupled method solution with rate γ

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