Energy norm analysis of exactly symmetric mixed finite elements for linear elasticity
نویسندگان
چکیده
We consider mixed finite element methods for linear elasticity which the symmetry of stress tensor is exactly satisfied. derive a new quasi-optimal priori error estimate uniformly valid with respect to compressibility. For posteriori analysis we Prager-Synge hypercircle principle and introduce in incompressible limit. All estimates are validated by numerical examples.
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,...
متن کاملMixed finite elements for elasticity
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...
متن کاملRectangular Mixed Finite Elements for Elasticity
We present a family of stable rectangular mixed finite elements for plane elasticity. Each member of the family consists of a space of piecewise polynomials discretizing the space of symmetric tensor fields in which the stress field is sought, and another to discretize the space of vector fields in which the displacement is sought. These may be viewed as analogues in the case of rectangular mes...
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 کاملSymmetric and conforming mixed finite elements for plane elasticity using rational bubble functions
The date of receipt and acceptance will be inserted by the editor Summary We construct stable, conforming and symmetric finite elements for the mixed formulation of the linear elasticity problem in two dimensions. In our approach we add three divergence free rational functions to piecewise polynomials to form the stress finite element space. The relation with the elasticity elements and a class...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2022
ISSN: ['1088-6842', '0025-5718']
DOI: https://doi.org/10.1090/mcom/3784