Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity
نویسندگان
چکیده
منابع مشابه
Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity
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,...
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This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, an...
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We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.
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This article considers a mixed finite element method for linear elasticity. It is based on a modified mixed formulation that enforces the continuity of the stress weakly by adding a jump term of the approximated stress on interior edges. The symmetric stress are approximated by nonconforming linear elements and the displacement by piecewise constants. We establish (h) error bound in the (broken...
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There have been many efforts, dating back four decades, to develop stablemixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector fields in which the displ...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2011
ISSN: 0036-1429,1095-7170
DOI: 10.1137/10080018x