A family of mixed finite elements for the elasticity problem
Numerische Mathematik
A Local Regularization Operator for Triangular and Quadrilateral Finite Elements
SIAM Journal on Numerical Analysis
A Mixed Finite Element Method for Elasticity in Three Dimensions
Journal of Scientific Computing
Lower Order Rectangular Nonconforming Mixed Finite Elements for Plane Elasticity
SIAM Journal on Numerical Analysis
A Unified Analysis of Several Mixed Methods for Elasticity with Weak Stress Symmetry
Journal of Scientific Computing
Conforming Rectangular Mixed Finite Elements for Elasticity
Journal of Scientific Computing
Rectangular mixed elements for elasticity with weakly imposed symmetry condition
Advances in Computational Mathematics
Journal of Scientific Computing
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The lowest order nonconforming rectangular element in three dimensions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement. With a modest increase in the number of degrees of freedom (24 for the stress), we obtain a conforming rectangular element for linear elasticity in three dimensions. Moreover, unlike the conforming plane rectangular or simplicial elements, this element does not involve any vertex degrees of freedom. Second, we remark that further low order elements can be constructed by approximating the displacement with rigid body motions. This results in a pair of conforming elements with 72 degrees of freedom for the stress and 6 degrees of freedom for the displacement.