Nonconforming Mixed Elements for Elasticity
نویسندگان
چکیده
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.
منابع مشابه
To appear in Mathematical Methods and Models in the Applied Sciences 12 (2002) NONCONFORMING MIXED ELEMENTS FOR ELASTICITY
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.
متن کاملPublications of Douglas N. Arnold
• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...
متن کاملA Mixed Nonconforming Finite Element for Linear Elasticity
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...
متن کاملNonconforming Tetrahedral Mixed Finite Elements for Elasticity
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...
متن کاملAnalysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
In this work, some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed. A uniform optimal convergence rate is established at the incompressible limit ν = 0.5 for both displacement and stresses (or pressure in the case of incompressible flow).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002