A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
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
Journal of Scientific Computing
| Hi-index | 0.00 |
We present a family of mixed methods for linear elasticity that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces, solve a symmetric positive-definite system. The design and analysis of this method is motivated by a new set of unisolvent degrees of freedom for symmetric polynomial matrices. These new degrees of freedom are also used to give a new simple calculation of the dimension of the space of polynomial symmetric matrix fields with vanishing normal traces and zero divergence on a tetrahedron. Such a dimension count was important in the development of the symmetric $H(\mathrm{div})$ conforming methods found in [D. N. Arnold, G. Awanou, and R. Winther, Math. Comp., 77 (2008), pp. 1229-1251].