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Conforming Rectangular Mixed Finite Elements for Elasticity
Shaochun Chen,Ya-Na Wang +1 more
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A new family of rectangular mixed finite elements for the stress-displacement system of the plane elasticity problem is presented and it is proved that they are stable and error estimates for both the stress field and the displacement field are obtained.Abstract:
We present a new family of rectangular mixed finite elements for the stress-displacement system of the plane elasticity problem. Based on the theory of mixed finite element methods, we prove that they are stable and obtain error estimates for both the stress field and the displacement field. Using the finite element spaces in this family, an exact sequence is established as a discrete version of the elasticity complex in two dimensions. And the relationship between this discrete version and the original one is shown in a commuting diagram.read more
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Convergence analysis of a new mixed finite element method for Biot's consolidation model
TL;DR: In this article, a mixed finite element method for the two-dimensional Biot's consolidation model of poroelasticity is proposed, which uses the total stress tensor and fluid flux as primary unknown variables as well as the displacement and pore pressure.
Journal ArticleDOI
A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
Jun Hu,Shangyou Zhang +1 more
TL;DR: In this article, a family of stable mixed finite elements for the linear elasticity on tetrahedral grids is constructed, where the stress is approximated by symmetric H(div)-P petertodd k−1 polynomial tensors and the displacement is estimated by C� −1-P�k€ p€ 1 polynomials, for all k ⩽ 4.
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A family of conforming mixed finite elements for linear elasticity on triangular grids
Jun Hu,Shangyou Zhang +1 more
TL;DR: In this paper, a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations is presented, and the wellposedness condition and the optimal a priori error estimate are proved for this family of finite elements.
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Finite element approximations of symmetric tensors on simplicial grids in ℝn: The lower order case
Jun Hu,Shangyou Zhang +1 more
TL;DR: Arnabels et al. as discussed by the authors constructed lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension.
Journal ArticleDOI
A Simple Conforming Mixed Finite Element for Linear Elasticity on Rectangular Grids in Any Space Dimension
TL;DR: A family of lower-order rectangular conforming mixed finite elements, in any space dimension, that shape function spaces for both stress and displacement are independent of the spatial dimension is constructed.
References
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A rotated nonconforming rectangular mixed element for elasticity
TL;DR: In this article, a low-order nonconforming mixed element for plane elasticity on rectangular meshes is presented, which is related to a discrete version of the elasticity differential complex with a non-conforming H2 element related to the rotated Q1 element.
Journal ArticleDOI
Anisotropic conforming rectangular elements for elliptic problems of any order
TL;DR: In this paper, two sets of C^N^-^1 conforming rectangular elements for linear elliptic problems of order 2N, N>=1, are presented, and the anisotropic error estimates are proved by the Newton's formulas for Hermite interpolation in two dimensions and the special properties of the divided differences with coincident knots.