Rectangular mixed elements for elasticity with weakly imposed symmetry condition
TL;DR: New rectangular mixed finite elements for linear elasticity are presented based on a modification of the Hellinger–Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a Lagrange multiplier.
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Abstract: We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger---Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a Lagrange multiplier. The elements are analogues of the lowest order elements described in Arnold et al. (Math Comput 76:1699---1723, 2007). Piecewise constants are used to approximate the displacement and the rotation. The first order BDM elements are used to approximate each row of the stress field.
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Citations
Mixed finite elements for elasticity on quadrilateral meshes
TL;DR: A stable family of methods for planar linear elasticity on general quadrilateral meshes, indexed by an integer r ≥ 2 and with rate of convergence in the L2 norm of order r for all the variables is developed.
32
Two Remarks on Rectangular Mixed Finite Elements for Elasticity
TL;DR: It is remarked that further low order elements can be constructed by approximating the displacement with rigid body motions and results in a pair of conforming elements with 72 degrees offreedom for the stress and 6 degrees of freedom for the displacement.
31
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A multipoint stress mixed finite element method for elasticity on simplicial grids
TL;DR: A new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids using the lowest order Brezzi-Douglas-Marini finite element spaces for the stress and the vertex quadrature rule in order to localize the interaction of degrees of freedom.
22
Towards a unified analysis of mixed methods for elasticity with weakly symmetric stress
TL;DR: Stable mixed methods are obtained by combining Stokes stable and elasticity stable finite elements and can be used to analyze most existing mixed methods for the linear elasticity problem with elementary techniques.
20
Domain decomposition and multiscale mortar mixed finite element methods for linear elasticity with weak stress symmetry
TL;DR: In this paper, two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry, and the condition number of the resulting algebraic interface problem is analyzed for both methods.
16
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