A family of mixed finite elements for linear elasticity

1989 ◽  
Vol 55 (6) ◽  
pp. 633-666 ◽  
Author(s):  
Mary E. Morley
Keyword(s):  
Finite Elements ◽  
Linear Elasticity ◽  
Mixed Finite Elements

Error indicators for mixed finite elements in 2-dimensional linear elasticity

1995 ◽  
Vol 127 (1-4) ◽  
pp. 345-356 ◽  
Author(s):  
Dietrich Braess ◽  
Ottmar Klaas ◽  
Rainer Niekamp ◽  
Erwin Stein ◽  
Frank Wobschal
Keyword(s):  
Finite Elements ◽  
Linear Elasticity ◽  
Mixed Finite Elements ◽  
Error Indicators

scholarly journals Stable mixed finite elements for linear elasticity with thin inclusions

2020 ◽  
Author(s):  
W. M. Boon ◽  
J. M. Nordbotten
Keyword(s):  
Finite Elements ◽  
Linear Elasticity ◽  
A Priori ◽  
Mixed Finite Elements ◽  
Stability And Convergence ◽  
Discretization Schemes ◽  
Weighted Norms ◽  
Discrete Differential Operator ◽  
Mechanics Of Composite Materials ◽  
Well Posed

Abstract We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of hierarchically connected manifolds is formed which we refer to as mixed-dimensional. The governing equations with respect to linear elasticity are then defined on this mixed-dimensional geometry. The resulting system of partial differential equations is also referred to as mixed-dimensional, since functions defined on domains of multiple dimensionalities are considered in a fully coupled manner. With the use of a semi-discrete differential operator, we obtain the variational formulation of this system in terms of both displacements and stresses. The system is then analyzed and shown to be well-posed with respect to appropriately weighted norms. Numerical discretization schemes are proposed using well-known mixed finite elements in all dimensions. The schemes conserve linear momentum locally while relaxing the symmetry condition on the stress tensor. Stability and convergence are shown using a priori error estimates and confirmed numerically.

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