Constructs exact finite element sub-complexes for the conformal complex on tetrahedra, producing discrete TT tensors with shown inf-sup stability for H(div) symmetric traceless elements paired with discontinuous vectors.
A family of conforming mixed finite elements for linear elasticity on triangular grids
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full $C^0$-$P_k$ space enriched by $(k-1)$ $H(\d)$ edge bubble functions on each internal edge, while the displacement field by the full discontinuous $P_{k-1}$ vector-valued space, for the polynomial degree $k\ge 3$. The main challenge is to find the correct stress finite element space matching the full $C^{-1}$-$P_{k-1}$ displacement space. The discrete stability analysis for the inf-sup condition does not rely on the usual Fortin operator, which is difficult to construct. It is done by characterizing the divergence of local stress space which covers the $P_{k-1}$ space of displacement orthogonal to the local rigid-motion. The well-posedness condition and the optimal a priori error estimate are proved for this family of finite elements. Numerical tests are presented to confirm the theoretical results.
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UNVERDICTED 4representative citing papers
Explicit closed-form enrichments and Airy potentials yield a concrete Hsieh-Clough-Tocher-type C^1 space whose image is exactly the Arnold-Douglas-Gupta stress space, enabling global explicit elasticity complexes and new C^1 elements on barycentric refinements.
A coupled mixed-Lagrange finite element formulation for linear elasticity is shown to be well-posed with optimal a priori error estimates even when the mixed-element subdomain has diameter O(h).
Strong enforcement of symmetry in H(div)-conforming finite elements yields material-robust stress approximations independent of the constitutive law, whereas weak enforcement produces arbitrarily poor results even in zero-stress cases with anisotropic laws.
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Finite elements for symmetric and traceless tensors in three dimensions
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Explicit closed-form enrichments and Airy potentials yield a concrete Hsieh-Clough-Tocher-type C^1 space whose image is exactly the Arnold-Douglas-Gupta stress space, enabling global explicit elasticity complexes and new C^1 elements on barycentric refinements.
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Strong enforcement of symmetry in H(div)-conforming finite elements yields material-robust stress approximations independent of the constitutive law, whereas weak enforcement produces arbitrarily poor results even in zero-stress cases with anisotropic laws.